If x dollars are invested at 10% for 6 years, the future value of the investment is given by S(x)=x+0.6x.

Question

 If x dollars are invested at 10% for 6 years, the future value of the investment is given by S(x)=x+0.6x.
a. Find the inverse of the function.
b. What do the outputs of the inverse function represent?
c. Use this function to find the amount of money that must be invested for 6 years at 10% to have a future value of $24,000.

Answer 1

Nicole,

 

To find the inverse of S(x):

 

1) Replace S(x) by y.

2) Exchange x for y and y for x at the same time.

3) Solve the resulting equation for y.

4) The expression for y will be the inverse for S(x).

 

Here are the details:

 

1) y = x + 0.6 x = 1.6 x

2) x = 1.6 y

3) y = x/1.6 = 0.625 x

4) S^-1(x) = 0.625 x  (the S^-1 is the notation for the inverse)

 

b) Since x represents the amount of money invested at 10% for 6 years, and S(x) represents its future value, the inverse works in reverse. If x represents the future value, then S^-1(x) will be the amount of money required to achieve it after 6 years. This is called the present value.

 

c) Set x = 24000 in S^-1(x) and calculate the answer: S^-1(24000) = 0.625 × 24000 = 15000. the answer is $15,000.