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?

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

a negative exponent is translated as follows:

so, we have