Answer:
120
Step-by-step explanation:
We are given that the function for the number of students enrolled in a new course is [tex]f(x) = 4^{x}-1[/tex].
It is asked to find the average increase in the number of students enrolled per hour between 2 to 4 hours.
We know that the average rate of change is given by,
[tex]A = \frac{f(x)-f(a)}{x-a}[/tex],
where f(x)-f(a) is the change in the function as the input value (x-a) changes.
Now, the number of students enrolled at 4 = f(4) = [tex]f(x) = 4^{4}-1[/tex] = 255 and the number of students enrolled at 2 = f(2) = [tex]f(x) = 4^{2}-1[/tex] = 15
So, the average increase [tex]A=\frac{f(4)-f(2)}{4-2}[/tex] = [tex]A=\frac{255-15}{4-2}[/tex] = [tex]A=\frac{240}{2}[/tex] = 120.
Hence, the average increase in the number of students enrolled is 120.
