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The population of a city is modeled by the function
y = 35000(0.94) {}^(t)where y is the population of the city after t years starting in the year 2000 in what year will the population be 5,000

User GamefanA
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1 Answer

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Solution

The population of a city is modeled by the function


y=35000(0.94)^t

where y is the population of the city after t years starting in the year 2000


y=35000(0.94)^t

In what year will the population be 5000


\begin{gathered} y=35000(0.94)^t \\ when\text{ y =5000} \\ t=? \end{gathered}
\begin{gathered} y=35000(0.94)^t \\ 5000=35000(0.94)^6 \\ (5000)/(35000)=(35000)/(35000)(0.94)^t \\ (1)/(7)=0.94^t \end{gathered}
\begin{gathered} ln0.1428=ln(0.94)^t \\ ln0.1428=tln(0.94) \\ -1.946=t(-0.06188) \\ t=-(1.946)/(-0.06188) \\ t=31.448 \\ t\approx32 \end{gathered}

Therefore in 32 years time the population will be 5000

User IBhavin
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