Question

The cost of a chocolate bar is $0.48 now. The price of the chocolate bar is increasing by 2 percent annually. Model the price of the chocolate bar as a function of time.

Answer 1

Recall that the equation for exponential growth can be written as

`\begin{gathered} y=I(1+r)^t \\ \text{where} \\ I\text{ is the initial value} \\ r\text{ is the rate of growth} \end{gathered}`

Given that the initial value of the chocolate bar is $0.48, and the rate increases by 2% annually. Then we have the following variables

I = 0.48

r = 0.02 (from 2%)

Then the equation to model the price of the chocolate bar is

`C(t)=0.48(1+0.02)^t`