Year 10 Interactive Maths - Second Edition

Modelling Exponential Growth

For example, if you invest A₀ at 5% per annum compound interest for n years, then the amount will grow by 5% every year. If A_n is the amount of the investment after n years, then:

Example 20

Form an exponential relation for an investment of A₀ that increases at 8% per annum for n years.

Solution:

Let A_n be the amount after n years.

So, A_n = 1.08ⁿA₀

Example 21

Form an exponential relation for the population, P₀, of a certain city that increases at the rate of 24% per annum for n years.

Solution:

Example 22

Form an exponential relation for the value of a house if the value is expected to rise at 16% per annum over a period of n years.

Solution:

Key Terms

exponential growth