Question

Enrollment in a school district is currently 1250 students and is decreasing at approximately 3% per year. Enter the number of years it will take the school district enrollment to reach 1000 students. Round your answer to the nearest tenth. Years

Answer 1

Answer: the number of years is 7.3 years

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 1250

A = 1000

r = 3% = 3/100 = 0.03,

Therefore

1000 = 1250(1 - 0.03)^t

1000/1250 = (0.97)^t

0.8 = 0.97^t

Taking log of both sides, it becomes

Log 0.8 = tLog 0.97

- 0.0969 = - 0.0132t

t = - 0.0969/- 0.0132t

t = 7.3 years