The population P (in thousands) of a city from 1990 - 2005 can be modeled by P = 375.55e^-0.01052t, where t is the great, b with t=0 corresponding to 1990. According to the model, during what year will the population be approximately 300,000?

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Mathematics

26 December, 10:20

The population P (in thousands) of a city from 1990 - 2005 can be modeled by P = 375.55e^-0.01052t, where t is the great, b with t=0 corresponding to 1990. According to the model, during what year will the population be approximately 300,000?

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Alisa Williamson · Answer 1

Population model

P=375.55e^ (-0.01052t)

we are required to find t when p=300000.

substituting the values in formula and solving for t we get:

300000=375.55e^ (-0.01052t)

this will give us

798.828385=e^ (-0.01052t)

getting the natural log of both sides will be:

6.683146136=0.01052t

t=635.28~635

Given that t=0 in 1990, the population would be 300000 in the years 2625