Exponential Functions

NZ Level 7 (NZC) Level 2 (NCEA)

Transforming Exponential Expressions

Consider the function $f\left(t\right)=2\left(\frac{3}{8}\right)^t$`f`(`t`)=2(38)`t`, where $t$`t` represents time.

a

What is the initial value of the function?

b

Express the function in the form $f\left(t\right)=2\left(1-r\right)^t$`f`(`t`)=2(1−`r`)`t`, where $r$`r` is a decimal.

c

Does the function represent growth or decay of an amount over time?

growth

A

decay

B

growth

A

decay

B

d

What is the rate of decay per time period? Give the rate as a percentage.

Easy

Approx 2 minutes

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