Question

The population of coyotes in the northwestern portion of Alabama is given by the formula p (t )equals (t squared plus 100 )ln (t plus 2 )​, where t represents the time in years since 2000​ (the year 2000 corresponds to t equals 0 ). Find the rate of change of the coyote population in 2002 ​(tequals2​).

Answer 1

The rate of change of the Coyote population in 2002 is 32

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