Chapter 7.6, Problem 18PPE

To determine

To find: the investment worth after 30 years.

Answer to Problem 18PPE

The investment worth after 30 years is 40000.

Explanation of Solution

Given information:

An investment of $5000 doubles in value every decade. The function $f\left(x\right)=5000\cdot 2^x$ , where $x$ is the number of decades, models the growth of the value of the investment.

Calculation:

Consider the function,

  $f\left(x\right)=5000\cdot 2^x$

Now, solve the function as shown,

  $\begin{array}{c}f\left(x\right)=5000\cdot 2^x\\ f\left(3\right)=5000\left(2^3\right)\\ =5000\left(8\right)\\ =40000\end{array}$

So, the investment worth after 30 years is 40000.