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

Answer:

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

Part 2) $305,602\ people$

Step-by-step 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

$y=140,000(1.05)^{16}=305,602\ people$