Question

A sales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. The representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months.

1.8(1.02)^12t

What does the value 1.8 represent?

A.
the monthly percent increase in the total number of members at the club
B.
the number of new members that join the club per month
C.
the initial number of club members, in hundreds
D.
the growth factor that reveals the rate at which the total number of members at the club increases

Answer 1

C. the initial number of club members, in hundreds

Explanation:

The general form of such an expression is ...

(initial value)×(growth factor per period)^(number of periods)

The use of 12 in the exponent suggests that the growth factor of 1.02 is an annual factor. If that is the case, for t months, the membership should be modeled as ...

1.8(1.02^(t/12))

_____

As written, the expression is not an exponential expression. With appropriate parentheses, it might be a good model if t is the number of years (not months), and if the expected growth rate is 2% per month.

1.8(1.02^(12t))