Exponential Functions

NZ Level 6 (NZC) Level 1 (NCEA)

Growth and Decay

Lesson

Compound interest is an example of exponential growth because it increases by a power or index which, when we graph it, gives it this kind of shape:

The formula we use to solve questions involving exponential growth is the same as the compound interest formula:

$A=P\left(1+r\right)^n$`A`=`P`(1+`r`)`n`

A country's population of $18$18 million people is expected to increase by $2.1%$2.1% p.a. over the next $38$38 years .

Calculate the expected population in $38$38 years time.

Round your answer to the nearest whole number.

This is basically the opposite of exponential growth, where things *decrease* in value at an exponential rate. The graphs look something like this:

The formula we use to solve questions involving exponential decay is the same as the depreciation formula:

$A=P\left(1-r\right)^n$`A`=`P`(1−`r`)`n`

The area covered by an ice shelf was measured over some warmer months. At the beginning of the first month the ice shelf was spread over an area of $1437$1437 square kilometres, and it was found that this area decreased by $2%$2% each month over the recording period.

What area was covered by the ice shelf after $13$13 months of recording? Give your answer to the nearest square kilometre.

Using the rounded value from the previous part, what was the loss in the ice shelf's area over $13$13 months?

Apply everyday compounding rates

Apply numeric reasoning in solving problems