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?

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.

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

number of subscribers the year before.

Step-by-step 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

step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is