{"id":2134,"date":"2026-05-25T13:38:43","date_gmt":"2026-05-25T08:08:43","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=2134"},"modified":"2026-05-25T13:38:47","modified_gmt":"2026-05-25T08:08:47","slug":"ncert-class-9-maths-exercise-2-4-solutions-linear-growth-and-decay","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-2-4-solutions-linear-growth-and-decay\/","title":{"rendered":"NCERT Class 9 Maths Exercise 2.4 Solutions \u2013 Linear Growth and Decay"},"content":{"rendered":"<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2134?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2134?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 2.4 explains the concepts of <strong>linear growth<\/strong> and <strong>linear decay<\/strong> using real-life situations like plant growth, mobile depreciation, population increase, and prepaid balance reduction. These detailed step-by-step solutions help students understand linear functions and algebraic modelling easily.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Topic<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Chapter<\/td><td>Introduction to Linear Polynomials<\/td><\/tr><tr><td>Exercise<\/td><td>Exercise 2.4<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Class<\/td><td>Grade 9<\/td><\/tr><tr><td>Main Concepts<\/td><td>Linear Growth &amp; Linear Decay<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><tr><td>Useful For<\/td><td>School Exams &amp; Olympiad Preparation<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Linear Growth<\/li>\n\n\n\n<li>Linear Decay<\/li>\n\n\n\n<li>Linear Functions<\/li>\n\n\n\n<li>Algebraic Expressions<\/li>\n\n\n\n<li>Table of Values<\/li>\n\n\n\n<li>Depreciation<\/li>\n\n\n\n<li>Population Growth<\/li>\n\n\n\n<li>Balance Reduction<\/li>\n\n\n\n<li>Mathematical Modelling<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Linear Growth Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=a+bx<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"323\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-27-1024x323.png\" alt=\"image\" class=\"wp-image-2135\" title=\"NCERT Class 9 Maths Exercise 2.4 Solutions \u2013 Linear Growth and Decay\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-27-1024x323.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-27-300x95.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-27-768x243.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-27.png 1178w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Linear Decay Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mo>\u2212<\/mo><mi>b<\/mi><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=a-bx<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"327\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-28-1024x327.png\" alt=\"image\" class=\"wp-image-2136\" title=\"NCERT Class 9 Maths Exercise 2.4 Solutions \u2013 Linear Growth and Decay\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-28-1024x327.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-28-300x96.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-28-768x245.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-28.png 1166w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Depreciation Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Value<\/mtext><mo>=<\/mo><mtext>Initial&nbsp;Value<\/mtext><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mtext>Decrease&nbsp;per&nbsp;year<\/mtext><mo>\u00d7<\/mo><mtext>Years<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Value} = \\text{Initial Value} &#8211; (\\text{Decrease per year} \\times \\text{Years})<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Population Growth Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><msub><mi>P<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>r<\/mi><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P = P_0 + rt<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-Step Solutions<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Find the height after 7 months<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Initial height = 1.75 feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Monthly growth = 0.5 feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After 7 months:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1.75<\/mn><mo>+<\/mo><mn>7<\/mn><mo stretchy=\"false\">(<\/mo><mn>0.5<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">1.75 + 7(0.5)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>1.75<\/mn><mo>+<\/mo><mn>3.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 1.75 + 3.5<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>5.25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 5.25<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Height after 7 months = <strong>5.25 feet<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii) Table of Values<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Month (t)<\/th><th>Height h (feet)<\/th><\/tr><\/thead><tbody><tr><td>0<\/td><td>1.75<\/td><\/tr><tr><td>1<\/td><td>2.25<\/td><\/tr><tr><td>2<\/td><td>2.75<\/td><\/tr><tr><td>3<\/td><td>3.25<\/td><\/tr><tr><td>4<\/td><td>3.75<\/td><\/tr><tr><td>5<\/td><td>4.25<\/td><\/tr><tr><td>6<\/td><td>4.75<\/td><\/tr><tr><td>7<\/td><td>5.25<\/td><\/tr><tr><td>8<\/td><td>5.75<\/td><\/tr><tr><td>9<\/td><td>6.25<\/td><\/tr><tr><td>10<\/td><td>6.75<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii) Expression relating h and t<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>1.75<\/mn><mo>+<\/mo><mn>0.5<\/mn><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">h = 1.75 + 0.5t<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This represents <strong>linear growth<\/strong> because the height increases by a constant amount every month.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A mobile phone is bought for \u20b910,000. Its value decreases by \u20b9800 every year.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Find value after 3 years<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Initial value = \u20b910,000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Decrease every year = \u20b9800<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After 3 years:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>10000<\/mn><mo>\u2212<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>800<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">10000 &#8211; 3(800)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>10000<\/mn><mo>\u2212<\/mo><mn>2400<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 10000 &#8211; 2400<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>7600<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 7600<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Value after 3 years = <strong>\u20b97600<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii) Table of Values<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Year (t)<\/th><th>Value v (\u20b9)<\/th><\/tr><\/thead><tbody><tr><td>0<\/td><td>10000<\/td><\/tr><tr><td>1<\/td><td>9200<\/td><\/tr><tr><td>2<\/td><td>8400<\/td><\/tr><tr><td>3<\/td><td>7600<\/td><\/tr><tr><td>4<\/td><td>6800<\/td><\/tr><tr><td>5<\/td><td>6000<\/td><\/tr><tr><td>6<\/td><td>5200<\/td><\/tr><tr><td>7<\/td><td>4400<\/td><\/tr><tr><td>8<\/td><td>3600<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii) Expression relating v and t<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>v<\/mi><mo>=<\/mo><mn>10000<\/mn><mo>\u2212<\/mo><mn>800<\/mn><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">v = 10000 &#8211; 800t<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This represents <strong>linear decay<\/strong> because the value decreases by a fixed amount every year.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Population after 6 years<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Initial population = 750<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Increase per year = 50<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After 6 years:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>750<\/mn><mo>+<\/mo><mn>6<\/mn><mo stretchy=\"false\">(<\/mo><mn>50<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">750 + 6(50)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>750<\/mn><mo>+<\/mo><mn>300<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 750 + 300<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>1050<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 1050<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Population after 6 years = <strong>1050<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii) Table of Values<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Year (t)<\/th><th>Population P<\/th><\/tr><\/thead><tbody><tr><td>0<\/td><td>750<\/td><\/tr><tr><td>1<\/td><td>800<\/td><\/tr><tr><td>2<\/td><td>850<\/td><\/tr><tr><td>3<\/td><td>900<\/td><\/tr><tr><td>4<\/td><td>950<\/td><\/tr><tr><td>5<\/td><td>1000<\/td><\/tr><tr><td>6<\/td><td>1050<\/td><\/tr><tr><td>7<\/td><td>1100<\/td><\/tr><tr><td>8<\/td><td>1150<\/td><\/tr><tr><td>9<\/td><td>1200<\/td><\/tr><tr><td>10<\/td><td>1250<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii) Expression relating P and t<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mn>750<\/mn><mo>+<\/mo><mn>50<\/mn><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P = 750 + 50t<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This represents <strong>linear growth<\/strong> because population increases by a constant number every year.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A telecom company charges \u20b9600 for a recharge scheme. This prepaid balance reduces by \u20b915 every day after recharge.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Equation for remaining balance<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Initial balance = \u20b9600<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduction every day = \u20b915<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>b<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>600<\/mn><mo>\u2212<\/mo><mn>15<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b(x)=600-15x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This represents <strong>linear decay<\/strong> because balance decreases by a fixed amount daily.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii) After how many days will balance become zero?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>600<\/mn><mo>\u2212<\/mo><mn>15<\/mn><mi>x<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">600 &#8211; 15x = 0<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>15<\/mn><mi>x<\/mi><mo>=<\/mo><mn>600<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">15x = 600<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>40<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 40<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Balance will run out after <strong>40 days<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii) Table of Values<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Days (x)<\/th><th>Balance b(x)<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>585<\/td><\/tr><tr><td>2<\/td><td>570<\/td><\/tr><tr><td>3<\/td><td>555<\/td><\/tr><tr><td>4<\/td><td>540<\/td><\/tr><tr><td>5<\/td><td>525<\/td><\/tr><tr><td>6<\/td><td>510<\/td><\/tr><tr><td>7<\/td><td>495<\/td><\/tr><tr><td>8<\/td><td>480<\/td><\/tr><tr><td>9<\/td><td>465<\/td><\/tr><tr><td>10<\/td><td>450<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u274c Using wrong sign in growth and decay problems<br>\u274c Forgetting initial value in expressions<br>\u274c Calculation mistakes in tables<br>\u274c Confusing increase with decrease<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u2714 Growth means addition (+)<br>\u2714 Decay means subtraction (\u2212)<br>\u2714 Write formula before solving<br>\u2714 Make tables carefully and systematically<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. Which expression represents linear growth?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>20<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500-20x<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1000<\/mn><mo>+<\/mo><mn>50<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">1000+50x<\/annotation><\/semantics><\/math>1000+50x<br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2+5<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mi>x<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1000<\/mn><mo>+<\/mo><mn>50<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">1000+50x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. Which expression represents linear decay?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>200<\/mn><mo>+<\/mo><mn>15<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">200+15x<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>10<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500-10x<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2-1<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">3x^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>10<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500-10x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. A value decreases by \u20b9100 every year. Which expression is correct?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>500<\/mn><mo>+<\/mo><mn>100<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500+100x<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>100<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500-100x<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>100<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>500<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">100x-500<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>500<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>100<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500-100x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. Linear growth means:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) Variable increase<br>B) Constant increase<br>C) Random increase<br>D) Quadratic increase<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) Constant increase<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. What is linear growth?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Linear growth means a quantity increases by a fixed amount over equal intervals.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. What is linear decay?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Linear decay means a quantity decreases by a fixed amount over equal intervals.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. What is a linear function?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A function represented by a straight-line equation is called a linear function.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Why are tables important in linear functions?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Tables help us understand patterns and relationships clearly.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. Can real-life situations be represented using linear equations?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Yes, many daily-life situations can be represented using linear equations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Practice more chapter-wise Maths solutions, MCQs, mock tests, and concept-based exercises on <strong><a target=\"_blank\" rel=\"noreferrer noopener\">MyMockMate<\/a><\/strong> and strengthen your Class 9 Mathematics preparation with smart learning resources!<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2134?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2134?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p> Short Intro Exercise 2.4 explains the concepts of linear growth and linear decay using real-life<\/p>\n","protected":false},"author":1,"featured_media":2137,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[22,4,11],"tags":[668,697,136,711,703,685,708,706,709,704,705,91,674,707,712,710,713],"class_list":["post-2134","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","category-class-9","category-maths-class-9","tag-algebraic-expressions","tag-class-9-algebra","tag-class-9-maths","tag-depreciation-problems","tag-exercise-2-4-solutions","tag-grade-9-mathematics","tag-growth-and-decay-maths","tag-linear-decay-questions","tag-linear-functions","tag-linear-growth-and-decay","tag-linear-growth-examples","tag-maths-chapter-2-solutions","tag-mymockmate-maths-solutions","tag-polynomial-chapter-solutions","tag-population-growth-questions","tag-table-of-values-maths","tag-telecom-recharge-balance-problems"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=2134"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2134\/revisions"}],"predecessor-version":[{"id":2138,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2134\/revisions\/2138"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/2137"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=2134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=2134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=2134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}