Question

P(t) = 250 * (3.04)^t/1.98,

The function above was used to model the approximate population, of rabbits in the area t years after January 1, 2010. According to this model, what best describes how the rabbits population changed in the area?.

Answer 1

The concept which best describes the change of the population is the derivative of
`p(t)=250(3.04)^{(t)/(1.98)}`.

Explanation:

Observe that the function
`p(t)=250(3.04)^{(t)/(1.98)}` describes the amount of rabbits at the time t (in years) but no the rate of change of the population at a given instant. So you have to use the derivative of
`p(t)` to obtain that rate of change at any instant. For example, if we derivate the function
`p(t)=250(3.04)^{(t)/(1.98)}` we obtain:

`p'(t)=250\cdot \log((1)/(1.98))(3.04)^{(t)/(1.98)}`

And if we want to find the rate of change at
`t=5` years we evaluate

`p'(5)=250\cdot \log((1)/(1.98))(3.04)^{(5)/(1.98)}=2326` rabbits/year