Question

The number of exercises on Khan academy has increased rapidly since it began in 2006. The relationship between the elapsed time, t, in years, since Khan academy began, and the total number of its exercises, E year (t), is modeled by the following function:

E year (t)=100⋅(1.7)^t
Complete the following sentence about the monthly rate of change in the number of exercises. Round your answer to two decimal places.

A. The monthly rate of change in the number of exercises is 100⋅(1.7)^t
.
B. The monthly rate of change in the number of exercises is 1.7^t

C. The monthly rate of change in the number of exercises is ( 100⋅(1.7)^t ) / 12

​D. The monthly rate of change in the number of exercises is ( 100⋅(1.7)^t ) / 30

​
.

Answer 1

The monthly rate of change in the number of exercises on Khan Academy, based on the given function, is represented by taking the annual rate and dividing it by 12. Therefore, the correct answer is (100 · (1.7)^t) / 12.

Step-by-step explanation:

The student's question about the monthly rate of change in the number of exercises on Khan Academy, given the function E year (t) = 100 · (1.7)^t, can be answered by understanding the concept of exponential growth rate. This function models the total number of exercises after t years since 2006. The correct option to express the monthly rate is to divide the annual growth by 12 because there are 12 months in a year. Therefore, the monthly rate of change is the annual rate of change divided by 12, which corresponds to option C: (100 · (1.7)^t) / 12.