Question

She had 8 subscribers at the beginning of the month. One month later, her number of subscribers doubled and continued to double each month. Create a function to model the growth in the number of subscribers to the singer's channel since the month it had 8 subscribers. What is a reasonable domain in this situation?

Answer 1

`f(x)= 8(2)^x`

Explanation:

She had 8 subscribers at the beginning of the month. One month later, her number of subscribers doubled and continued to double each month

when month =0 the subscribers = 8 (0,8)

month =1 , subscribers = 16 (1,16)

month = 2, subscribers = 32 and so on (2,32)

Subscribers are doubled every month

For exponential growth we use formula y=ab^x

where 'a' is the initial value. given initial value is 8 so a=8

To frame the function , we plug in (1,16) a=8 and solve for b

`y = ab^x`

`16 = 8b^1`

divide by 8 on both sides

b^1 = 2 so b= 2

Exponential function becomes (a=8, b= 2)

`y = ab^x`

`f(x)= 8(2)^x`

She had 8 subscribers at the beginning of the month

So when month x=0 then the number of subscribers = 8

Domain x starts from 0 month and it goes on increasing

Domain x be the number of months.