Question

The population of Mathloversville is given by the equation P=38e^0.095t , where t is the number of years from now. How long will it take the population to reach 1 million?

Answer 1

Approximately 107years

Explanation:

Given the population of Mathloversville modelled by the equation P=38e^0.095t where t is the number of years from now.

To find the time it will take the population to reach 1million from now, we will substitute P = 1,000,000 into the equation given

1,000,000 = 38e^0.095t

Dividing both sides by 38

1,000,000/38 = e^0.095t

Taking the ln of both sides

ln(1,000,000/38) = ln e^0.095t

ln26,315.79 = 0.095t

10.18 = 0.095t

t = 10.18/0.095

t = 107.16years

It will take approximately 107years for the population to reach 1million