Suppose that an isolated island is initially populated by r 0 = 1,702 rabbits. Assume a logistic growth model, and suppose that the growth rate a = 40 and that the carrying capacity is R = 8,790: (a)...

Suppose that an isolated island is initially populated by r₀
= 1,702 rabbits. Assume a logistic growth model, and suppose that the growth rate a = 40 and that the carrying capacity is R = 8,790:

(a) Estimate the number of rabbits at time t = 1:

 (b) Suppose the initial estimate is uncertain and that repeated counting shows that the actual initial number is between 1;500 and 1;900: Provide an upper and lower estimate for the number of rabbits at time t = 1:

 (c) Suppose also that the growth rate is uncertain but that we estimate it to be greater than 30 and less than 50: Give a new upper an lower estimate.

 (d) The carrying capacity is also uncertain but is in the interval ranging from 7,000 to 10,000: Give a new upper and lower estimate.]