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,
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