A wildlife management research team is introducing a rabbit

A wildlife management research team is introducing a rabbit population into a forest for the first time. The population will be controlled by wolves and other predators and can be modeled by the function r(t)= 1260/0.4+27.6(2.6)^-0.065t

A)How many rabbits did the wildlife management research team bring into the forest?

B)How many rabbits can be expected after 10 weeks?

C)How many rabbits can be expected after the first year?

D)How many rabbits can be expected after 4 years? 5 years?What can the researchers expect the rabbit population to approach as time goes on?

E)They can expect __ nothing rabbits after 4 years

F)They can expect __ nothing rabbits after 5 years

G)The rabbit population approaches ___ nothing as time goes on.

Solution

r = 1260 / (0.4 + 27.6(2.6)^(-0.065t))

a) Plug in t = 0 :
1260 / (0.4 + 27.6)
45

45 rabbits

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10 weeks :
Plug in t = 10 for 10 weeks and we get..

1260 / (0.4 + 27.6(2.6)^(-0.065*10))

83 rabbits

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1 year :
Plug in t = 52 for 52 weeks...

1260 / (0.4 + 27.6(2.6)^(-0.065*52))

844 rabbits

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4 yrs :
Plug in t = 52*4 = 208 weeks...

1260 / (0.4 + 27.6(2.6)^(-0.065*208))

3149 rabbits

5 yrs :
Plug in t = 260

1260 / (0.4 + 27.6(2.6)^(-0.065*260))

3150 rabbits

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As time goes on,
the no of rabbits approaches

3150