The number of students at a local university increased from 2,500 students to 5,000 students in 10 years. Based on a geometric mean,the university grew at an average percentage rate of
A)2,500 students per year.
B)1.072 percent per year.
C)7.2 percent per year.
D)250 students per year.

Question

Quizplus · Accepted Answer

To find the average percentage rate of growth, we need to use the geometric mean formula:

Geometric mean = [(Ending value / Beginning value)^(1/number of years)] - 1

Plugging in the given values, we get:

Geometric mean = [(5,000 / 2,500)^(1/10)] - 1
Geometric mean = (2)^(1/10) - 1
Geometric mean = 0.072 or 7.2%

Therefore, the university grew at an average percentage rate of 7.2% per year. Choice C is the correct answer.

The Number of Students at a Local University Increased from 2,500