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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
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