Question

A) In 2000, the population of a country was approximately 5.82 million and by 2040 it is projected to grow to 9 million. Use the exponential growth model A=A0e^kt, in which t is the number of years after 2000 and A0 is in millions, to find an exponential growth function that models the data.

B) By which year will the population be 15 million?

Answer 1

By 2086

Explanation:

The provided equation is:

`A=A0*e^(k*t)` , where:

A=total of population after t years

A0=initial population

k= rate of growth

t= time in years

Given information:

The final population will be 15 million, then A=15.

We start in 2000 with a 5.82 million population, then A0=5.82.

Missing information:

Although k is not given, we can calculate k by using the following statement, from 2000 to 2040 (within 40 years) population is proyected to grow to 9 million, which means a passage from 5.8 to 9 million (3.2 million increament).

Then we can use the same expression to calculate k:

`A=A0*e^(k*t)`

`9=5.8*e^(40*k)`

`ln(9/5.8)/40=k`

`0.010984166494596147=k`

`0.011=k`

Now that we have k=0.011, we can find the time (t) by which population will be 15 million:

`A=A0*e^(k*t)`

`15=5.8*e^(0.011t)`

`ln(15/5.8)/0.011=t`

`86.38111668634878=t`

`86.38=t`

Because the starting year is 2000, and we need 86.38 years for increasing the population from 5.8 to 15 million, then by 2086 the population will be 15 million.