Question

Write an exponential function to model the following situation.

A population of 140,000 grows 5% per year for 16 years.
How much will the popluation be after 16 years?
Write an exponential function in terms of x.
y=
0
Write an exponential function in terms of x

Answer 1

Part 1) The exponential function is
`y=140,000(1.05)^x`

Part 2)
`305,602\ people`

Explanation:

Part 1) Write an exponential function

we know that

The exponential growth function is given by the formula

`y=a(1+r)^x`

where

y is the population

x is the number of years

a is the initial population

r is the rate of change

we have

`a=140,000\ people\\r=5\%=5/100=0.05`

substitute

`y=140,000(1+0.05)^x`

`y=140,000(1.05)^x`

Part 2) How much will the population be after 16 years?

For x=16 years

substitute the value of x in the exponential function

`y=140,000(1.05)^(16)=305,602\ people`