Joshua owns a cell phone company. With the addition of more store locations, the number of phones that his company sells increases exponentially. He determines the increase can be represented with this function.

Question

p
(
n
)
=
400
(
1.7
)
n

In this function, n is the number of locations and p(n) is the number of phones sold at n locations. After further review, Joshua finds that his function is incorrect. What change should he make to the function if he determines the rate of increase is correct but that the number of phones the function shows being sold is too high?

A.
Increase the base that is currently 1.7.

B.
Increase the coefficient that is currently 400.

C.
Decrease the coefficient that is currently 400.

D.
Decrease the base that is currently 1.7.

Answer 1

If Joshua finds that the number of phones sold according to his function \( p(n) = 400(1.7)^n \) is too high, he needs to adjust the coefficient in front of the function.

The coefficient of 400 represents the initial number of phones sold when there are 0 locations, and increasing it would result in an even higher number of phones sold. Therefore, to make the function reflect a lower number of phones sold, he should:

C. Decrease the coefficient that is currently 400.

This will yield a lower initial value and thereby reduce the total number of phones sold.