Question

The number of subscribers to a streaming video service doubles each week.

The function f(x) = 2* represents the number of subscribers in week x. When
are there 64 subscribers?

A. Week 6
B. Week 32
c. Week 4
D. Week 7
SUBMIT

Answer 1

Explanation:

This is an exponential equation that is solved by taking the natural log of both sides. The equation is

`f(x)=2^x`

If we are looking for x when f(x) = 64, then

`64=2^x`

Take the natural log of both sides:

`ln(64)=ln(2^x)`

The rules of logs allows us to bring the x down in front:

`ln(64)=xln(2)`

Divide both sides by ln(2) to get:

`(ln(64))/(ln(2))=x`

Do this on your calculator to get that x = 6.

You could also have just gone right to your calculator and started raising 2 to consecutive powers starting at like 3 or 4 to eventually get that 2 to the 6th power is equal to 64, but for the basics of solving log equations, you need to know how to do this.

Answer 2

A.
`\displaystyle Week\:6`

Step-by-step explanation:

`\displaystyle 64 = 2^x \\ \\ log_264 = x; 6 = x`

I am joyous to assist you anytime.