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: 3]

The average attendance increased exponentially by 4% each year for the three years from 2016 to 2019.
In 2019 the average attendance was 1631.
Find the average attendance for 2016.

1450 or 1449 to 1450
M2 for $1631=k\left(1+\frac4{100}\right)^3$ oe
or B1 for $\left(1+\frac4{100}\right)^3$ oe seen
or M1 for $1631=k\left(1+\frac4{100}\right)^n, n>0$ oe

[Maximum number: 3]

Dhanu has a model railway.

The value of Dhanu's model railway is $ 550.

This value increases exponentially at a rate of r % per year.
At the end of 5 years the value will be $ 736.
Calculate the value of r.
r=

6[.00] or 5.999...
M2 for $\sqrt[5]{\frac{736}{550}}$ .
OR M1 for $736=550x^5$ .

[Maximum number: 6]

(a)

Xavier buys a car for $ 2500.

The value of the car decreases exponentially at a rate of 10% each year.
Calculate the value of Xavier's car at the end of 5 years.
Give your answer correct to the nearest dollar.

[ 3 ]

1476 cao
B2 for 1480 or 1476.2...
OR M1 for $2500\left(1-\frac{10}{100}\right)^5$ oe

(b)

The number of a certain type of bacteria increases exponentially at a rate of r% each day. After 22 days, the number of this bacteria has doubled.
Find the value of r.
r=

[ 3 ]

3.20 or 3.200 to 3.201
M2 for $(\ldots)=\sqrt[22]{2}$ oe
or M1 for $N(\ldots)^{22}=2N$

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Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (b)