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Sagot :
Explanation:
The exponential growth function has the form
[tex]N\left(t\right)=N_0e^{kt}[/tex]Where N0 is the population for t = 0, k is a constant, and t is the number of years.
When t = 0, the population is 143,230, so
[tex]N\left(t\right)=143230e^{kt}[/tex]To find k, we will use the given information that when t = 10, the population N(t) = 217,325. So, by replacing these values and solving for k, we get:
[tex]\begin{gathered} 217325=143230e^{k\left(10\right)} \\ \frac{217325}{143230}=e^{10k} \\ 1.52=e^{10k} \\ \ln1.52=\ln e^{10k} \\ 0.4169=10k \\ \frac{0.4169}{10}=k \\ 0.04169=k \end{gathered}[/tex]Therefore, the equation that models the population growth is
[tex]N\left(t\right)=143230e^{0.04169t}[/tex]Finally, to predict the population of the city in 2016, we need to replace t = 16, so
[tex]\begin{gathered} N\left(16\right)=143230e^{0.04169\left(16\right)} \\ N\left(16\right)=279,079.116 \end{gathered}[/tex]Answer:
So, the answers are
[tex]N\left(t\right)=143230e^{0.04169t}[/tex]Population in 2016: 279,079.116
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