Question

The number of students enrolled in a new course as a function of time can be represented by the function. f(x)=(4)^x−1 What is the average increase in the number of students enrolled per hour between hours 2 and 4?

Answer 1

It seems that the function is f(x) = 4^ (x - 1).

Using that function, you can determine the number of students enrolled at hours 2 and 4.

The number of students enrolled at hour 2 is f(2),

f(2) = 4^ (2 - 1) = 4

The number of students enrolled at hour 4 is f(4),

f(4) = 4^(4 - 1) = 4^3 = 64

So the average increase is [64 - 4] students / [ 4 - 2 ] hours = 60students / 2hours = 30 students / hour.

If the function is not f(x) = 4^(x - 1) but f(x) = 4^x - 1, then the numbers are:

f(2) = 4^2 - 1 = 16 - 1 = 15

f(4) = 4^4 - 1 = 256 - 1 = 255

Average increase = (255 - 15) / (4 - 2) = 240 / 2 = 120 students/hour