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Short Intro

Exercise 2.4 explains the concepts of linear growth and linear decay 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.

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Quick Information Box

Topic	Details
Chapter	Introduction to Linear Polynomials
Exercise	Exercise 2.4
Subject	Mathematics
Class	Grade 9
Main Concepts	Linear Growth & Linear Decay
Difficulty Level	Moderate
Useful For	School Exams & Olympiad Preparation

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Concepts Used (Topics Covered)

• Linear Growth
• Linear Decay
• Linear Functions
• Algebraic Expressions
• Table of Values
• Depreciation
• Population Growth
• Balance Reduction
• Mathematical Modelling

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Important Formulas

Linear Growth Formula

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Linear Decay Formula

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Depreciation Formula

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Population Growth Formula

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Questions & Step-by-Step Solutions

Question 1

Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month.

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(i) Find the height after 7 months

Solution

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(ii) Make a table of values for t varying from 0 to 10 months and
show how the height, h, increases every month.

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(iii) Find an expression that relates v and t, and explain why it
represents linear growth.

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Question 2

A mobile phone is bought for ₹10,000. Its value decreases by ₹800 every year.

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(i) Find the value of the phone after 3 years.

Solution

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(ii) Make a table of values for t varying from 0 to 8 years and
show how the value of the phone, v, depreciates with time.

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(iii) Find an expression that relates v and t, and explain why it represents linear decay.

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Question 3

The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.

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(i) Find the population of the village after 6 years.

Solution

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(ii) Make a table of values for t varying from 0 to 10 years and show how the population, P, increases every year.

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(iii) Find an expression that relates P and t, and explain why it represents linear growth.

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Question 4

A telecom company charges 600 for a certain recharge scheme. This prepaid balance is reduced by15 each day after the recharge.

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(i) Write an equation that models the remaining balance b(x) after using the scheme for x days. Explain why it represents linear decay.

Solution

Reduction every day = ₹15$$b(x)=600-15x$$

This represents linear decay because balance decreases by a fixed amount daily.

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(ii) After how many days will the balance run out?

Solution

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(iii) Make a table of values for x varying from 1 to 10 days and
show how the balance b(x), reduces with time.

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Common Mistakes

❌ Using wrong sign in growth and decay problems
❌ Forgetting initial value in expressions
❌ Calculation mistakes in tables
❌ Confusing increase with decrease

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Exam Tips

✔ Growth means addition (+)
✔ Decay means subtraction (−)
✔ Write formula before solving
✔ Make tables carefully and systematically

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Practice MCQs

1. Which expression represents linear growth?

A) $500-20x$
B) $1000+50x$1000+50x
C) $x^2+5$
D) $2^x$

Answer

✅ B) $1000+50x$

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2. Which expression represents linear decay?

A) $200+15x$
B) $500-10x$
C) $x^2-1$
D) $3x^2$

Answer

✅ B) $500-10x$

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3. A value decreases by ₹100 every year. Which expression is correct?

A) $500+100x$
B) $500-100x$
C) $100x-500$
D) $500x$

Answer

✅ B) $500-100x$

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4. Linear growth means:

A) Variable increase
B) Constant increase
C) Random increase
D) Quadratic increase

Answer

✅ B) Constant increase

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FAQ Section

Q1. What is linear growth?

Linear growth means a quantity increases by a fixed amount over equal intervals.

Q2. What is linear decay?

Linear decay means a quantity decreases by a fixed amount over equal intervals.

Q3. What is a linear function?

A function represented by a straight-line equation is called a linear function.

Q4. Why are tables important in linear functions?

Tables help us understand patterns and relationships clearly.

Q5. Can real-life situations be represented using linear equations?

Yes, many daily-life situations can be represented using linear equations.

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