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Exponential growth occurs if an initial amount has a regular
percentage increase after a certain period of time.
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 An 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 An be the amount after n years.
So, An = 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
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