The rabbit population on a small island is modeled by the function p(t)= -0.8t^4
ID: 2876832 • Letter: T
Question
The rabbit population on a small island is modeled by the function p(t)= -0.8t^4 + 1200t + 1000, where t is the time (in months) since observations of the island began. Use calculus to answer parts (b), (d), and (e). Find the initial rabbit population. Find the time when the growth rate of the population is equal to zero. Find the population when the growth rate is zero. Round your answer to a whole number. Find the t-intervals where the population increases and decreases during the first year. Determine whether the population reaches a maximum or minimum value during the first year. Support your answer.Explanation / Answer
Gven P(t) = - 0.8t4 + 1200t + 1000
a) at t =0 , P(0) = 0+0+1000 = 1000 ntial population of rabbit
b) dP(t)/dt = d/dt(- 0.8t4 + 1200t + 1000) = - 3.2t3 + 1200
dP(t)/dt = 0
- 3.2t3 + 1200 = 0
3.2t3 = 1200
t3 = 375
t = 7.21 minuts
at t=7.21 minuts grwth rate of population is zero
3) at t=7.21 mnuts
P(7.21) = - 0.8(7.21)4 + 1200(7.21) + 1000
= 7490.12
d) P(t) increasing for (7.21, infinity)
P(t) decreasing for (- infinity , 7.21)
e) at t=7.21 , P(7.21) = 7490.12 reaches maximum