Population Growth The resident populations P (in thousands) of Wisconsin fron 2000 through 2009 can be modeled by the exponential function
P(t) = 5382(1.0057)t
where t is the time in years with t = 0 corresponding to 2000.Use the model to estimate the population in the year (a) 2016 and (b) 2025.

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DarcySea DarcySea · Answer 1 · 2020-01-22T05:04:10+01:00

Answer:

(a) 5894 thousand

(b) 6204 thousand

Step-by-step explanation:

Given:

The expression for population growth of the residents of Wisconsin is given as:

[tex]P(t)=5382(1.0057)^t[/tex]

For the year 2000, the time is, [tex]t=0[/tex]

(a) Population in 2016.

Difference in years from 2000 to 2016 = 2016 - 2000 = 16 years.

Therefore, the time 't' for 2016 is equal to 16 years.

Now, plug in 16 for 't' in the above expression and solve for population 'P'. This gives,

[tex]P(t)=5382(1.0057)^t[/tex]

[tex]P(16)=5382(1.0057)^{16}\\\\P(16)=5894.4\approx 5894\ thousands[/tex]

Therefore, the estimated population of the residents in 2016 is 5894 thousand.

(b) Population in 2025.

Difference in years from 2000 to 2025 = 2025 - 2000 = 25 years.

Therefore, the time 't' for 2025 is equal to 25 years.

Now, plug in 25 for 't' in the above expression and solve for population 'P'. This gives,

[tex]P(t)=5382(1.0057)^t[/tex]

[tex]P(25)=5382(1.0057)^{25}\\\\P(25)=6203.8\approx 6204\ thousands[/tex]

Therefore, the estimated population of the residents in 2016 is 6204 thousand.