Question

There are currently 502 students at Hendrick Middle School. If that number is continuously

increasing at a rate of 2% per year, when will there be 926 students at the school? (Hint! When
working the problem, round all numbers to the thousandths place)

Answer 1

In the next 31 years

Explanation:

In this question, we are tasked with calculating the number of years it will take for a school’s population to reach a certain amount of it is increasing at a certain rate.

We can use a mathematical exponential approach to solve this.

Let’s say;

P = I( 1 + r)^t

where P is the projected population at 926

I is the initial population at 502

r is the percentage change or rate at 2% which is same as 2/100 = 0.02

and t is time

Plugging these values, we have

926 = 502(1 + 0.02)^t

Divide through by 502

1.845 = 1.02^t

take the logarithm of both sides

log 1.845 = tlog 1.02

t = log 1.845/log 1.02

t = 30.9 = 31 years