Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
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 appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
