Question

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

Answer 1

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