Chapter 6.2, Problem 6E

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 6E

The values are $a=10$ and $r=40\%$ , and the function value at $t=5$ is $53.8$ .

Explanation of Solution

Giveninformation:

The exponential function is $y=10{\left(1+0.4\right)}^t$ .

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 $a=10$ and $r=0.4=40\%$ .

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

  $\begin{array}{l}y=10{\left(1+0.4\right)}^5\\ $ \Rightarrow y=10{(1.4)}^5=10(5.3782)$\Rightarrow y=53.782\end{array}$

Conclusion:

Therefore, rounding the answer to the nearest tenth, we have $y=53.8$ .