The population of a city is modeled by the equation P (t) = 256,114e0.25t where t is measured in years. If the city continues to grow at this rate, how many years will it take for the population to reach one million?

Answer: it take 5.448 years for the population to reach one million.

Step-by-step explanation:

The population of a city is modeled by the equation

P (t) = 256,114e0.25t

where t is measured in years.

For the population to reach 1000000, it means that

1000000 = 256114e0.25t

1000000/256114 = e0.25t

3.9045 = e0.25t

Taking ln of both sides of the equation, it becomes

Ln 3.9045 = Ln e0.25t

1.362 = 0.25t

t = 1.362/0.25

t = 5.448 years