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I am using Bay County, a county located in the state of Michigan. According to the U.S. Census Bay county had a population of 103,126 in 2019 and in 2020 it had 103,856. How much would it grow by 2039? How will I represent the growth assuming an exponential model? The picture attached is the excel I have to use. so if you have an equation to insert in a column just an equation that'll work!

I Am Using Bay County A County Located In The State Of Michigan According To The US Census Bay County Had A Population Of 103126 In 2019 And In 2020 It Had 1038 class=

Sagot :

Given:

The intial population in 2019 is, P₀ = 103126.

The final population in 2020 is, P = 103856.

The objective is to find the population in the year 2039.

Explanation:

The general exponential form of population growth is,

[tex]P=P_0\times e^{rt}\text{ . . . . . . . (1)}[/tex]

Here, t represents the time period.

To find t:

The value of t from 2019 to 2020 can be calculated as,

[tex]\begin{gathered} t=2020-2019 \\ t=1 \end{gathered}[/tex]

To find r :

On plugging the obtained values in equation (1),

[tex]\begin{gathered} 103856=103126\times e^{r(1)} \\ \frac{103856}{103126}=e^{r(1)} \\ \log (\frac{103856}{103126})=r \\ r=0.003 \end{gathered}[/tex]

To find population at 2039:

The time period t can be calculated as,

[tex]\begin{gathered} t=2039-2019 \\ t=20\text{ years} \end{gathered}[/tex]

Now, final population after 2019 can be calculated as,

[tex]undefined[/tex]

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