Growth & Decay: Challenge & Extension
Mathematics
GCSE Foundation
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet covering Growth & Decay through exponential graphs for GCSE Foundation students, including practice, problem solving, real-world applications, and extension questions.
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Growth & Decay: Challenge & Extension
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Read the key concept below before attempting the questions.
1.
Growth and decay are modeled by exponential functions of the form y = a(1 ± r)^x, where r is the rate of growth (positive) or decay (negative). Understanding how to interpret and manipulate these functions is essential for analyzing real-world data.
[4 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the value of y when x=3 for the exponential decay function y=100(0.8)^x.
[2 marks]2.
Plot the graph of y=3(1.2)^x for x from 0 to 5. (Use the grid provided.)
[3 marks]3.
If y=50(1.05)^x, find the value of x when y=100.
[3 marks]C
Problem Solving & Reasoning
Answer each question with detailed reasoning.
1.
A bacteria population starts at 200 and decreases by 15% each hour. Write an exponential decay model for the population after x hours. How many bacteria are left after 4 hours?
[4 marks]2.
A radioactive substance has a half-life of 10 years. Write the exponential decay formula for the remaining substance after x years, assuming an initial amount of 100g. How much remains after 30 years?
[4 marks]D
Real-world Applications
Apply exponential models to real situations.
1.
A bank account with an annual interest rate of 5% compounded annually starts with £1000. Write the exponential growth formula for the amount after x years. How much money will be in the account after 10 years?
[4 marks]2.
A town's population is decreasing at a rate of 3% per year. If the current population is 50,000, find the population after 8 years using an exponential decay model.
[4 marks]E
Challenge & Extension
Attempt these advanced problems to extend your understanding.
1.
Given the exponential decay function y=150(0.9)^x, determine the value of x when y=100. Then, plot this point on the graph.
[3 marks]2.
A substance decays exponentially with the formula y=200e^(-0.2x). Calculate the decay constant k if the half-life is 3.5 units. Write the decay formula in the form y=ae^{kx}.
[4 marks]F
Mixed Review
Answer these mixed questions to consolidate your understanding.
1.
A medicine reduces in concentration by 10% every hour. If the initial concentration is 500mg, what is the concentration after 6 hours?
[2 marks]2.
Identify and correct the mistake: The decay function y=200(1.05)^x models decrease over time.
[2 marks]G
Error Analysis
Study each incorrect statement and correct it.
1.
A student claims that (0.5)^x is exponential growth because the base is less than 1. Explain why this is incorrect and correct the statement.
[3 marks]2.
A graph of y=2(1.1)^x is drawn. The student says it shows decay. Is this correct? Justify your answer.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet