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Tanzania [10]
3 years ago
12

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

Mathematics
1 answer:
Alex17521 [72]3 years ago
5 0

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

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