CAIE IGCSE Mathematics Extended E1.17 Exponential Growth and Decay Questions

Practise modelling repeated percentage growth or decay, finding unknown rates and determining when a value first crosses a stated threshold.

Exam points

model repeated growth or decay as initial value × (1 ± rate ÷ 100)^time
rearrange the exponential model and take a root to determine an unknown periodic rate
test consecutive whole periods to identify when a population, value or mass first crosses a limit

Covered syllabus points

E1.17.1 Use exponential growth and decay

[Maximum number: 2]

The number of trees in a forest is decreasing exponentially at a rate of 1.75% per year.
Eleven years ago there were 980 trees.
Calculate the number of trees in the forest now.
Give your answer correct to the nearest integer.

807
M1 for $980\left(1-\frac{1.75}{100}\right)^{11}$ oe or better

[Maximum number: 5]

The population of a town is 54000.
The population is decreasing exponentially at a rate of 2% per year.

(a)

Calculate the decrease in the population at the end of 4 years.

[ 3 ]

4192 or 4193

B2 for 49807 to 49808
or $\mathbf{M 2}$ for $54000-54000 \times\left(1-\frac{2}{100}\right)^{4}$ oe
or $\mathbf{M 1}$ for $54000 \times\left(1-\frac{2}{100}\right)^{4}$ oe

(b)

Find the number of complete years it takes for the population of 54000 to first fall below 44000.

[ 2 ]

11 nfww

M1 for $54000 \times\left(1-\frac{2}{100}\right)^{n}$ evaluated
with n=10 or n=11
or B1 for 10.1 or 10.13 to 10.14

[Maximum number: 3]

Carlos also buys a car with a value of $ 32500.

The value of the car decreases exponentially by 23% each year.
Find a formula for the value, $ V, of the car at the end of n years.

$V=32500 \times 0.77^{n}$ final
answer

B2 for answer $32500 \times 0.77^{n}$ or for correct explicit formula seen in working, may be unsimplified

or M1 for $32500 \times(1-0.23)^{n}$ oe seen or for correct implicit formula seen, may be unsimplified or answer of form $V=32500 \times k^{n}$

or answer of form $V=p \times(0.77 \mathrm{oe})^{n}$

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Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question 3