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The rabbit population on Park Point in Duluth, MN at time t is modeled by the r(t) = 225 cos pi/3 t + 425 where t is measured in years. ( Park Point, by the way, is reported as the world’s longest freshwater sand spit) What is the maximum number of rabbits on Park Point during a population cycle?


1. What is the maximum number of rabbits on Park Point during a population cycle?

2. How long is the population cycle?

3. Find the approximate number of rabbits on the island after 3.2 years

Respuesta :

Using the senoidal function, it is found that:

  • 1. The maximum number of rabbits on Park Point during a population cycle is of 650.
  • 2. The population cycle is of 3 years.
  • 3. The approximate number of rabbits on the island after 3.2 years is 205.

Senoildal function:

The function that models the population after t years is given by:

[tex]r(t) = 225\cos{\left(\frac{\pi}{3}\right)t} + 425[/tex]

Item 1:

The cosine function varies between -1 and 1, hence, considering it equals to 1:

[tex]r_{MAX} = 225 + 425 = 650[/tex]

The maximum number of rabbits on Park Point during a population cycle is of 650.

Item 2:

The period of a cosine function [tex]\cos{\frac{2\pi}{T}}[/tex] is T.

  • In this problem, T = 3, hence:

The population cycle is of 3 years.

Item 3:

[tex]r(3.2) = 225\cos{\left(\frac{\pi}{3}\right)3.2} + 425 = 205[/tex]

The approximate number of rabbits on the island after 3.2 years is 205.

You can learn more about senoidal functions at https://brainly.com/question/13575593

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