Question

A countries population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential growth formula round your answer to the nearest million. P=Ae^kt

Answer 1

The population in 2017 is 171 million

Explanation:

Let's assume population starts from 1991

so,

initial population is 147 million

so,
`A=147`

we can use formula

`P=Ae^(kt)`

we can plug A=147

`P=147e^(kt)`

In 1998:

t=1998-1991=7

`P=153`

now, we can plug these values into formula and find k

`153=147e^(7k)`

Divide both sides by 147

`(147e^(7k))/(147)=(153)/(147)`

`e^(7k)=(51)/(49)`

`\ln \left(e^(7k)\right)=\ln \left((51)/(49)\right)`

`k=(\ln \left((51)/(49)\right))/(7)`

`k=0.00572`

now, we can plug it back

and we get

`P=147e^(0.00572t)`

In 2017:

t=2017-1991=26

we can plug it and find P

`P=147e^(0.00572* 26)`

`P=170.57`

So,

The population in 2017 is 171 million