Chapter 6, Problem 16CR

To determine

To find: Whether the function represents exponential growth or exponential decay. Identify the percentage rate of change.

Answer to Problem 16CR

The function $y={(1.06)}^{8t}$represents exponential growth and the rate of growth is 59%.

Explanation of Solution

Given information: $y={(1.06)}^{8t}$

Calculation:

  $\begin{array}{}$ y={(1.06)}^{8t}$$ \Rightarrow y={({1.06}^8)}^t$$ \Rightarrow y\approx {(1.59)}^t$\end{array}$

The function is of the form $y=a{(1+r)}^t$ , where $1+r>1$ , so it represents exponential growth.

Using the growth factor $1+r$ to find the rate of growth,

  $\begin{array}{l}1+r=1.59\\ \Rightarrow r=1.59-1\\ \Rightarrow r=0.59\end{array}$

So, the rate of growth is 59%.

Thus, the function $y={(1.06)}^{8t}$represents exponential growth and the rate of growth is 59%.