Question

A country's population is described by the model: A = 1050e0.015t , where t is years. How long will it take the population to double? Round off to the nearest year.

Answer 1

Step 1:

In this question, we are given the following:

A country's population is described by the model:

`A=1050e^(0.015t)`

where t is years.

How long will it take the population to double?

Round off to the nearest year.

Step 2:

Now, double the population means that:

`1050\text{ x 2 = 2010}`

Then, we have that:

`\begin{gathered} 2010=1050e^(0.015t) \\ \text{Divide both sides by 1050, we have that:} \\ 2=e^(0.015t) \\ \text{Taking In of both sides, we have that:} \\ In\text{ 2 = 0.015t} \\ \text{Divide both sides by 0.015, we have that:} \end{gathered}`
`\begin{gathered} t\text{ =}\frac{In\text{ 2}}{0.015} \\ t\text{ = 46.20981204} \\ t\approx\text{ 46 ( to the nearest year)} \end{gathered}`

CONCLUSION:

The final answer is:

`46\text{ years ( to the nearest year)}`