the fox population in a certain region has a continuous growth rate of 9 percent per year. it is estimated…

the fox population in a certain region has a continuous growth rate of 9 percent per year. it is estimated that the population in the year 2010 was 8900. (a) find a function that models the population t years after 2010 (t = 0 for 2010). your answer is p(t) = (b) use the function from part (a) to estimate the fox population in the year 2017. your answer is (the answer must be an integer)

the fox population in a certain region has a continuous growth rate of 9 percent per year. it is estimated that the population in the year 2010 was 8900. (a) find a function that models the population t years after 2010 (t = 0 for 2010). your answer is p(t) = (b) use the function from part (a) to estimate the fox population in the year 2017. your answer is (the answer must be an integer)

Answer

Explanation:

Step1: Recall the continuous - growth formula

The formula for continuous growth is $P(t)=P_0e^{rt}$, where $P_0$ is the initial population, $r$ is the growth rate, and $t$ is the time in years. Given that $P_0 = 8900$ and $r=0.09$. So, $P(t)=8900e^{0.09t}$.

Step2: Calculate the value of $t$ for 2017

Since $t = 0$ for 2010, for the year 2017, $t=2017 - 2010=7$.

Step3: Substitute $t = 7$ into the population function

Substitute $t = 7$ into $P(t)=8900e^{0.09t}$. We get $P(7)=8900e^{0.09\times7}$. First, calculate $0.09\times7 = 0.63$. Then, $e^{0.63}\approx1.8776$. So, $P(7)=8900\times1.8776\approx16711$.

Answer:

(a) $P(t)=8900e^{0.09t}$ (b) $16711$