Question

Population Growth The resident populations P (in millions) of the united states from 1995 through 2010 can be modeled by the exponential function

p(t) = 254.75(1.01)t
Where t is the time in years,with t = 5 corresponding to 1995.Use the model to estimate the populations in the years(a) 2013 and (b) 2020.

Answer 1

The estimated populations in the years 2013 and 2020 are 320.262 and 343.365 respectively.

Explanation:

The resident populations P (in millions) of the united states from 1995 through 2010 can be modeled by the exponential function

`p(t)=254.75(1.01)^t`

Where t is the time in years,with t = 5 corresponding to 1995.

It means the initial year is 1990, ( 1995 - 5 = 1990).

Using this model we need to estimate the populations in the years 2013 and 2020.

2013 - 1990 = 23

Substitute t=23 in the given function.

`p(23)=254.75(1.01)^(23)\approx 320.262`

2020 - 1990 = 30

Substitute t=30 in the given function.

`p(30)=254.75(1.01)^(30)\approx 343.365`

Therefore, the estimated populations in the years 2013 and 2020 are 320.262 and 343.365 respectively.