the fox population in a certain region has a continuous growth rate of 6 percent per year. it is estimated…

the fox population in a certain region has a continuous growth rate of 6 percent per year. it is estimated that the population in the year 2000 was 5600.\n(a) find a function that models the population t years after 2000 (t = 0 for 2000).\nhint: use an exponential function with base e.\nyour answer is p(t) =\n(b) use the function from part (a) to estimate the fox population in the year 2008.\nyour answer is (the answer must be an integer)

the fox population in a certain region has a continuous growth rate of 6 percent per year. it is estimated that the population in the year 2000 was 5600.\n(a) find a function that models the population t years after 2000 (t = 0 for 2000).\nhint: use an exponential function with base e.\nyour answer is p(t) =\n(b) use the function from part (a) to estimate the fox population in the year 2008.\nyour answer is (the answer must be an integer)

Answer

Explanation:

Step1: Recall the exponential 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 = 5600) (population in 2000, when (t = 0)) and (r=0.06) (6% growth rate, since (6%=\frac{6}{100}=0.06)). So, (P(t)=5600e^{0.06t})

Step2: Calculate the population in 2008

For the year 2008, (t = 2008 - 2000=8) Substitute (t = 8) into the function (P(t)=5600e^{0.06t}) (P(8)=5600e^{0.06\times8}=5600e^{0.48}) We know that (e^{0.48}\approx1.6160744) (P(8)=5600\times1.6160744\approx9049.91664)

Answer:

(a) (P(t)=5600e^{0.06t}) (b) (9050)