Can anyone solve this and show me the steps too? I need it for studying, thanks.

Question

If the growth in the population of a rabbits is P(t) = 800e^0.08z and P is population at time (t) measured in weeks. (show steps please)

a) Find the initial population of the rabbits.

b) Calculate how many rabbits are there after 2 weeks (14 days).

c) Calculate the rate of change of rabbits after 2 weeks (14 days).

Answer 1

P(0) = 800 rabbits initially in week 0

P(2) = 800e^.08(2) = 800e(.16) = about 938.8 = about 939 rabbits in 2 weeks

P'(t) = 800(.08)e^.08t = 64e^.08t

P'(2) = 64e^.16 = 75.1

P'(1) = 800.08(e^.08) = 64e^.08= 69.3

P'(3) = 800.08(e^.24) = 81.3

(69.3 + 81.3) = 150.6 = 75.3= average rate of change from t=1 to t=3 which is the same 75 as the instantaneous rate of change at t=2 weeks, rounded off to nearest integer

P'(0) = 64

P'(2) = 75

add them = 139

800 = 139 = 939 rabbits in week two