Question

A social networking site currently has 400,000 active members, and that figure is predicted to increase by 32% each year. The following expression represents the number of active members on the site after t years. 400,000(1.32)^t

The approximate monthly growth rate of the number of active members on the site can be modeled by an expression in the given form.
A^bt



Determine the values of a and b that reveal the approximate monthly growth rate of the number of active members on the site.
A.
a = 12 and b = 1.023
B.
a = 1.32 and b = 12
C.
a = 1.023 and b = 12
D.
a = 12 and b = 1.32

Answer 1

C. A = 1.023 and B = 12

Explanation:

We are given ,

The expression representing the number of active members after t years is,

`400,000(1.32)^t`

i.e.
`400,000(1+0.32)^t`

So, the expression showing the number of active members monthly;y is,

`400,000(1+(0.32)/(12))^(12t)`

i.e.
`400,000(1.023)^(12t)`

Now, the monthly growth rate is modeled by the expression
`A^(bt)`.

On comparing the expression, we get that,

A= 1.023

B= 12

Thus, option C is correct.