Question

A cable company uses the formula S = 20,000 (1 + 0.08)y to estimate the number of subscribers, S, that use their service after y years. If there were 20,000 cable television subscribers when the cable company began, what is the meaning of the expression (1 + 0.08)Y?

Answer 1

Options :

A. Every year the number of subscribers is estimated to increase by 8 over the number

of subscribers the year before.

B. Every year the number of subscribers is estimated to increase by 8% of the original

20,000 subscribers

C. Every year the number of subscribers is estimated to increase by 8% over the

number of subscribers the year before.

D. Every year the number of subscribers is estimated to increase by 80% of the

original 20,000 subscribers.

Answer:

C. Every year the number of subscribers is estimated to increase by 8% over the

number of subscribers the year before.

Explanation:

Given that:

The formula represents an exponential function :

S = 20,000 (1 + 0.08)^y

General form of an exponential equation :

y(x) = ab^x

Where a = initial value ; b = rate of change ; x = time

Comparing the formula given with the general equation:

a = 20000 = Number of subscribers when company began

b^x = (1 + 0.08)^y = percentage increase in the number of subscribers over y years