Answer:
The rate of change of the Coyote population in 2002 is 32
Step-by-step explanation:
Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2
The formula is given as;
P(t) = (t^2 + 100) ln (t + 2)
The rate of change refers to the first integral of the formula;
Thus we need to calculate this by the use of product formula;
The first differential of t^2 + 100 is 2t
while that of ln(t + 2) is 1/(t + 2)
P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)
Now, we substitute 2 for the value of t here.
P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))
P’(2) = 4 ln 4 + 104(1/4)
P’(2) = 4ln 4 + 26
P’(2) = 5.55 + 26 = 31.55 which is approximately 32
