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) 1.071 percent per year.
C) 7.1 percent per year.
D) 250 students per year.

Question

Quizplus · Accepted Answer

To find the average percentage growth rate using geometric mean, we use the formula:

Average growth rate = (Ending value / Beginning value)^(1/number of years) - 1

Here, the beginning value is 2,500 students, the ending value is 5,000 students, and the number of years is 10. So, substituting these values in the formula, we get:

Average growth rate = (5,000/2,500)^(1/10) - 1
Average growth rate = 1.071 - 1
Average growth rate = 0.071 or 7.1%

Therefore, the correct answer is choice C, 7.1 percent per year.

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