Question

1) A school has an enrollment of 1500 students. The student population is expected to increase at a rate of 2.6% each year for the next 5 years.

a) A What is the growth factor as a decimal?




b) Estimate the number of students enrolled 10 years from now. Round to the nearest student.

Show your work!!

Answer 1

The growth factor as a decimal is 1.026 and the number of students enrolled 10 years from now is 1939

How to determine the growth factor?

The given parameters are

Initial value of enrollment, a = 1500

Rate, r = 2.6%

The growth factor is then calculated as:

Growth factor = 1 + Rate

This gives

Growth factor = 1 + 2.6%

Evaluate the sum

Growth factor = 1.026

Hence, the growth factor as a decimal is 1.026

The number of students enrolled 10 years from now

As a general rule, the number of students enrolled t years from now is

Students = Initial value * Growth factor^Number of years

This is represented as

Students = 1500(1.026)^t

10 years from now means t = 10

So, we have

Students = 1500(1.026)^10

Evaluate

Students = 1939

Hence, the number of students enrolled 10 years from now is 1939

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