Solution
The population of a city is modeled by the function
[tex]y=35000(0.94)^t[/tex]where y is the population of the city after t years starting in the year 2000
[tex]y=35000(0.94)^t[/tex]In what year will the population be 5000
[tex]\begin{gathered} y=35000(0.94)^t \\ when\text{ y =5000} \\ t=? \end{gathered}[/tex][tex]\begin{gathered} y=35000(0.94)^t \\ 5000=35000(0.94)^6 \\ \frac{5000}{35000}=\frac{35000}{35000}(0.94)^t \\ \frac{1}{7}=0.94^t \end{gathered}[/tex][tex]\begin{gathered} ln0.1428=ln(0.94)^t \\ ln0.1428=tln(0.94) \\ -1.946=t(-0.06188) \\ t=-\frac{1.946}{-0.06188} \\ t=31.448 \\ t\approx32 \end{gathered}[/tex]Therefore in 32 years time the population will be 5000
