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

Answer:

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

Step-by-step explanation:

Observe that the function $p(t)=250(3.04)^{\frac{t}{1.98}}$ 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 $p(t)=250(3.04)^{\frac{t}{1.98}}$ we obtain:

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

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

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