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PLEASE HELP ASAP

A city starts with a population of 500,000 people in 2007. Its population declines according to the equation
P(t) = 500,000e -0.099t
where P is the population in t years later. Approximately when will the population be one-half the initial amount?

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Answer:

Step-by-step explanation:

Given the exponential function:

P(t) = 500,000 * e^(-0.099t)

P(t) = population t years later

When population will be one-half the initial amount

Half the initial amount = 500000/2 = 250,000

250000 = 500000 * e^(-0.099t)

250000/50000 = e^(-0.099t)

0.5 = e^(-0.099t)

Take the In of both sides

In(0.5) = - 0.099t

−0.693147 = - 0.099t

0.693147 / 0.099 = t

t =

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