Due in 45 minutes. Due Wed 09/27/2017 11:59 The fox population in a certain regi

ID: 3144866 • Letter: D

Question

Due in 45 minutes. Due Wed 09/27/2017 11:59 The fox population in a certain region has a relative growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 16300. a) Find a function that models the population t years after 2000 (t 0 for 2000). Pit) = Preview bi) Use the fiunction from part (a) to estimate the fox population in the year 2008. Round to the nearest fox. foxes Get help: Points possible: 4 This is attempt 1 of 3 Message instructor about this question License

Explanation / Answer

Solution

Let at t = 0, the year be represented by Y0 and the population of Y0 be represented by P(0).

Thus, one year after t = 0, will be Y0 and the corresponding population would be P(1). Generalizing, population t years after Y0 would be P(t).

Now, we are given Y0 = 16300 and annual growth rate = 6% or 0.06, in decimal form.

Part (a)

Population growth during Y0 = 16300 x 0.06 and hence

Population 1 year after Y0 = 16300 + (16300 x 0.06) = 16300 x 1.06 = P(1)

Population growth during Y1 = (16300 x 0.06) x 0.06 and hence

Population 2 years after Y0 = (16300 x 1.06) + {(16300 x 1.06) x 0.06}

= 16300 x 1.062 = P(2).

Generalizing, Population t years after Y0 = P(t) = 16300 x 1.06t= P(0) x 1.06tANSWER 1

Part (b)

Substituting P(0) = 16300, and t = 8,

Population in 2008 = 16300 x 1.068= 25979.72 or 25980 ANSWER 2