The exponential model A=11.4e^0.019t describes the​ population, A, of a country in​ millions, t years after 2003. Use the model to determine when the population of the country will be 18 million.

Answer 1

18 = 11.4e^0.019t

ln18 = (0.019t)(ln 11.4)

Can you solve for t and answer?

Answer 2

Let us first start by filling in all of the unknown variables into the equation and then we can solve for the variables we don't know.

The variable that we do know is A = 18 million because this is what shows the population of the country.

Substituting it in will make it look like:

18 = 11.4e^(0.019t)

Now the only thing we don't know in this equation is t so let us isolate and solve the variable.

18/11.4 = e^(0.019t)

ln(18/11.4) = 0.019t

ln(18/11.4)/0.019 = t

Now that we have t isolated we can solve the left hand side and get the answer.

∴ t = 24.04 which means the year is 2027

If you want to check the answer because you are unsure, you can always plug it back into the original equation.

A = 11.4e^(0.019(24.04))

A = 18

Answer 3

Hi Olivia R.

Question does 11.4 represent your starting point, such as 11.4 million in 2003 if so the info below should be useful?

A = 11.4e^0.019t

A = population

You are given A = 18 million

18 million = 11.4e^0.019t

You would use logarithms to solve for t can you continue from here, give it a try or let me know if you have further questions