CAIE IGCSE Mathematics Extended E1.17.1 Use Exponential Growth and Decay Questions

Work through Extended CAIE IGCSE Mathematics exponential models by applying compound multipliers and solving for unknown rates or periods.

Exam points

model exponential growth and decay using repeated percentage multipliers
calculate future or past values with a compound growth or decay factor
solve for a rate or number of periods and round the resulting population or value

[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

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CAIE IGCSE Mathematics Extended E1.17.1 Use Exponential Growth and Decay Questions question 1

Question (a)

Question (b)