word problem

Question

In an effort to control vegetation overgrowth, 115 rabbits are released in an isolated area free of predators. After
2 years, it is estimated that the rabbit population has increased to 1035. Assuming exponential population growth, what will the population be after another 6 months? Round to the nearest rabbit

Answer 1

 

 

   f(t) = C exp(Kt)

 

  f(0) = 115 --->  C = 115

 

  f(2) = 1035 ---->    115*exp(2k) = 1035

 

                                  exp(2k) = 1035/115 = 9

 

                                   2k = ln(9)

 

                                    k = ln(9)/2

 

    The function is f(t) = 115*exp( (ln(9)/2) t)

 

   For t=6 months,83835

 

        115*exp ( (ln(9)/2*6) = 115 * exp ( ln(9)*3 ) =