The number of students enrolled in a new course as a function of time can be represented by the function.

AngelRay
Nov 15, 2017

#2**+1 **

f(2) = 4^{2} - 1 = 16 - 1 = 15 At 2 hours, there are 15 students enrolled.

f(4) = 4^{4} - 1 = 256 - 1 = 255 At 4 hours, there are 255 students enrolled.

The number of students goes from 15 to 255 .

255 - 15 = 240 So the number of students increased by 240 .

The number of hours goes from 2 to 4 .

4 - 2 = 2 So the number of hours increased by 2 .

In 2 hours time, the number of students increased by 240 .

On average, that is an increase of 240/2 , or 120 , students per hour.

The average increase in the number of students per hour is 120 .

hectictar
Nov 15, 2017

#1**+1 **

For this, plug values 2 and 4 in for x.

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

\(f(2)=16-1, f(4)=256-1\)

\(f(2)=15, f(4)=255\)

For the average, add the two values and divide by 2.

\(\frac{15+255}{2}=\frac{270}{2}=135\)

So the average increase is 135 students.

AdamTaurus
Nov 15, 2017

#2**+1 **

Best Answer

f(2) = 4^{2} - 1 = 16 - 1 = 15 At 2 hours, there are 15 students enrolled.

f(4) = 4^{4} - 1 = 256 - 1 = 255 At 4 hours, there are 255 students enrolled.

The number of students goes from 15 to 255 .

255 - 15 = 240 So the number of students increased by 240 .

The number of hours goes from 2 to 4 .

4 - 2 = 2 So the number of hours increased by 2 .

In 2 hours time, the number of students increased by 240 .

On average, that is an increase of 240/2 , or 120 , students per hour.

The average increase in the number of students per hour is 120 .

hectictar
Nov 15, 2017