Chapter 6.2, Problem 11E

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 11E

The values are $a=6.72$ and $r=100\%$ , and the function value at $t=5$ is $215$ .

Explanation of Solution

Giveninformation:

The exponential function is $g(t)=6.72{\left(2\right)}^t$ .

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 $a=6.72$ and $1+r=2\Rightarrow r=1=100\%$ .

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

  $\begin{array}{l}g(5)=6.72{\left(2\right)}^5\\ \Rightarrow g(5)=6.72(32)\\ \Rightarrow g(5)=215.04\end{array}$

Conclusion:

Therefore, rounding the answer to the nearest tenth, we have $g(5)=215$ .