Question

The function for finding the population growth in Mayertowne is given by f(t) = 120(1.15)t. What is the rate of increase?

Answer 1

Remember that the equation formula for this is y = ab^x, which a = initial value and b = growth/decay.

Since this is an increase, you will be subtracting 1 from the growth percentage, which is 1.15. The quantity becomes 0.15.

To convert that into a percentage, just move the decimal 2 places to the right, which will be 15.

In short, the rate of increase is 15%.

Answer 2

$\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ \stackrel{A}{f(t)}=\stackrel{P}{120}(1.15)^t\implies f(t)=120(1+\stackrel{r}{0.15})^t \\\\\\ r\%=0.15\cdot 100\implies r=\stackrel{\%}{15}$