Respuesta :
Answer:
2016
Explanation:
Given the populations, P (in thousands) of a particular county from 1971 through 2014 modeled by the equation;
[tex]P=71.7e^{0.00345t}[/tex]If the population of the country reached 350,000, the time it will take to reach this population can be gotten as shown below;
[tex]\begin{gathered} 350=71.7e^{0.0345t} \\ \frac{350}{71.7}=e^{0.0345t} \\ 4.8815=e^{0.0345t} \end{gathered}[/tex]Take the natural logarithm of both sides
[tex]\begin{gathered} \ln (4.8815)=\ln e^{0.0345t} \\ \ln (4.8815)=0.0345t \\ \text{ }1.5854\text{= 0.0345t} \end{gathered}[/tex]Divide both sides by 0.0345;
[tex]\begin{gathered} \frac{1.5854}{0.0345}=\frac{0.0345t}{0.0345} \\ \text{Swap} \\ \frac{0.0345t}{0.0345}=\frac{1.5854}{0.0345} \\ t=\frac{1.5854}{0.0345} \\ t=45.95 \end{gathered}[/tex]This shows that the value of t is approximately 46 according to the calculation
Since at 1971, t = 1, at t = 46, the year it will take the population of the county to reach 350,000 is 2016
