Chapter 6.2, Problem 12E

To determine

To identify:The initial amount $a$ and the rate of growth $r$ (as a percent) of the exponential function. Evaluate the function when $t=5$ . Round your answer to the nearest tenth.

Answer to Problem 12E

The values are $a=1$ and $r=80\%$ , and the function value at $t=5$ is $21.7$ .

Explanation of Solution

Giveninformation:

The exponential function is $p(t)={1.8}^t$ .

Formula used:

The exponential growth function is

  $y=a{\left(1+r\right)}^t$

Where $a$ represents the initial amount, $y$ represents the final amount, $r$ represents the rate of growth in decimal form, and $t$ represents the time.

When compare the given exponential function with the general exponential growth function, we notice the values are $a=1$ and $1+r=1.8\Rightarrow r=0.8=80\%$ .

Now, evaluating the function at $t=5$ , we obtain

  $\begin{array}{l}p(5)={1.8}^5\\ \Rightarrow p(5)=21.67\end{array}$

Conclusion:

Therefore, rounding the answer to the nearest tenth, we have $p(5)=21.7$ .