Question

The population of foxes in a certain region over a 2-year period is estimated to be
P1(t) = 300 + 50 sin(πt/12)

in month t, and the population of rabbits in the same region in month t is given by
P2(t) = 4000 + 400 cos(πt/12)

.
Find the rate of change of the populations when t = 4. (Express a decrease in population as a negative rate of change. Round your answers to one decimal place.)

Answer 1

Hmmmm. precalculus. Wondering if you have had basic derivatives...
if so, p1' (rate)=50PI/12 cos(piT/12) put in t=4
and p2'(rate)=-400pi/12 sinPIt/12

Now if you have to do this with limits (UGH UGH UGH).

rate=(p1(t+dt)-p(t)/dt) lim as dt>>0

rate=(300 + 50 sin(πt/12+pidt/12)-300-50sin(Pit/12) /dt

now go use the sin(A+B) formula, and reduce it...fun, fun, fun and a tablet of paper...) It will reduce to the above.

Answer 2

7 wabbits