NCERT Class 9 Maths Exercise 2.4 Solutions – Linear Growth and Decay

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.

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

Concepts Used (Topics Covered)

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

Important Formulas

Linear Growth Formula

Linear Decay Formula

Depreciation Formula

Population Growth Formula

Questions & Step-by-Step Solutions

Question 1

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

(i) Find the height after 7 months

Solution

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

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

Question 2

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

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

Solution

(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.

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

Question 3

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

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

Solution

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

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

Question 4

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

(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 = ₹15b(x)=600−15xb(x)=600-15x

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

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

Solution

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

Common Mistakes

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

Exam Tips

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

Practice MCQs

1. Which expression represents linear growth?

A) 500−20x500-20x
B) 1000+50x1000+50x1000+50x
C) x2+5x^2+5
D) 2x2^x

Answer

✅ B) 1000+50x1000+50x

2. Which expression represents linear decay?

A) 200+15x200+15x
B) 500−10x500-10x
C) x2−1x^2-1
D) 3x23x^2

Answer

✅ B) 500−10x500-10x

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

A) 500+100x500+100x
B) 500−100x500-100x
C) 100x−500100x-500
D) 500x500x

Answer

✅ B) 500−100x500-100x

4. Linear growth means:

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

Answer

✅ B) Constant increase

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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