Question

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!

Answer 1

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,

$P=P_0\times e^{rt}\text{ . . . . . . . (1)}$

Here, t represents the time period.

To find t:

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

$\begin{gathered} t=2020-2019 \\ t=1 \end{gathered}$

To find r :

On plugging the obtained values in equation (1),

$\begin{gathered} 103856=103126\times e^{r(1)} \\ \frac{103856}{103126}=e^{r(1)} \\ \log (\frac{103856}{103126})=r \\ r=0.003 \end{gathered}$

To find population at 2039:

The time period t can be calculated as,

$\begin{gathered} t=2039-2019 \\ t=20\text{ years} \end{gathered}$

Now, final population after 2019 can be calculated as,

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