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A city had a population of 23,800 in 2007 and a population of 26,700 in 2012. Find the exponential growth function for the city. Use t=0 to represent 2007. (Round k to five decimal places) Use the growth function to predict the population of the city in 2022. Round to the nearest hundred

User Scribe
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1 Answer

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Given city had a a population of 23,800 in 2007 and a population of 26,700 in 2012. At t=0 is for year 2007,

We take,

Exponential growth function as:


N_0=N_0e^(kt)

At t=0


N_0=23,800

At t = 5,


N(5)=26700

Now,


\begin{gathered} (26700)/(23800)=(23800e^(k\cdot5))/(23800) \\ \ln 1.12=\ln e^(k\cdot5) \\ (\ln 1.12)/(5)=(k\cdot5)/(5) \\ (\ln 1.12)/(5)=k \end{gathered}

so,


k=0.1133

and


N(t)=22300e^(0.1133t)

b). At t=15,


\begin{gathered} N(15)=23,800e^(0.1133(15)) \\ \text{ =23300}*\text{5.}419 \\ =126273 \end{gathered}

Hence, population of the city in 2022 will be 126273.

User Lucas Trzesniewski
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