IDNLearn.com: Your reliable source for finding expert answers. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.
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
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.
