Chapter 7.6, Problem 14P

An investment of $8000 in a certain Certificate of Deposit $(\text{CD})$ doubles in value every seven years. The function that models the growth of this investment is $f(x)=8000\cdot 2^x,$

where $x$ is the number of doubling periods. If the investor does not withdraw any money from this CD, how much money will be available for withdrawal after 28 years?

To determine

To find the amount available for withdrawal from an CD(certificate of deposit ) after 28 years .

Answer to Problem 14P

The required amount that can be withdrawal after 28 years =$128000

Explanation of Solution

Given :

Here he has given that the deposited amount $8000 in CD that doubles within

Seven(7) years

And the function that models the growth of the investment is given by

  $f(x)={8000.2}^x$

Formula used:

Here the formula used is

  $f(x)={8000.2}^x$

Where x is the number of doubling periods

Calculation:

So using the above formula,

He will calculate the invested amount after 28 years

Since our amount double in seven years and we have to calculate amount after 28 years .

Hence x=28/7

=4 is the number of doubling period.

So in the above formula,put x=4 we get the answer

  $f(4)=8000.{(2)}^4=8000\times 16$ =$128000

Conclusion:

Hence the invested amount after 28 years will be =$128000