Question

A high school has a population of 2,035 students and is increasing by 3% each year.

a) Write an exponential function to model the student population in terms of the number of years from now.
b) predict the number of students that will be in school after five years.

Answer 1

a) y = 2,035(1.03)^t

b) 2,359

Explanation:

a)

Exponential growth:

y = a(1 + r)^t

where

y = future vale

a = initial value

r = periodic rate of growth

t = number of periods

y = 2,035(1 + 0.03)^t

y = 2,035(1.03)^t

b)

Here we have a = 2,035; r = 3% = 0.03; t = 5

y = 2,035(1 + 0.03)^5

y = 2,359

2,359