From everyday questions to specialized queries, IDNLearn.com has the answers. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

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


Sagot :

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