If the population of rabbits in a certain area is modeled by the function, r=10,000cos(pi/12t)+35,000 where t is the time in months, approximately how many rabbits will there be in August (January is equal to t = 1)?
To find the number of rabbits in a certain month using the given function, we need to substitute the value of t corresponding to that month into the equation. In this case, January corresponds to t = 1.
Let's calculate the value of t for August. Since January is t = 1, we need to find the number of months from January to August. There are 7 months between January and August:
August - January = 8 - 1 = 7
Now, we can substitute this value of t = 7 into the equation given:
r = 10,000cos(pi/12*7) + 35,000
First, let's calculate cos(pi/12 * 7):
cos(pi/12 * 7) = cos(7pi/12)
Using a scientific calculator or an online tool, calculate the cosine value of 7pi/12 (approximately 0.3584).
Substituting this value into the equation:
r = 10,000 * 0.3584 + 35,000
Now, calculate 10,000 * 0.3584 (approximately 3584).
r = 3584 + 35,000
Adding these values together:
r = 38,584
Therefore, the approximate number of rabbits in August is 38,584.