Question

In 2018, the number of students at The Villages High School was 975 and is increasing at a rate of 2.5% per year. Write and use an exponential growth function to project the populating in 2025. Round to the nearest whole number. Help plzzz

Answer 1

1,159 students

Explanation:

the exponential growth rate formula:

A = P ( 1 + r)ⁿ

• A = amount after growth = ??
• P = current/original amount = 975 students
• r = yearly growth rate = 2.5% or 0.025
• n = number of years = 2025 - 2018 = 7

Pop. 2025 = 975 (1 + 0.025)⁷

Pop. 2025 = 975 x 1.025⁷ = 1,158.97 ≈ 1,159 students

Answer 2

`A(t)=975(1.025)^t`

In 2025,the number of students at the villages high school=1159

Explanation:

We are given that in 2018

Number of students at the villages high school=975

Increasing rate,r=2.5%=0.025

We have to write and use of exponential growth function to project the populating in 2025.

`A_0=975,t=0`

According to question

Number of students at the villages high School is given by

`A(t)=A_0(1+r)^t`

Substitute the values

`A(t)=975(1+0.025)^t=975(1.025)^t`

t=7

Substitute the value

Then, the number of students at the villages high school in 2025

`A(7)=975(1.025)^7=1158.96\approx 1159`