question 7(multiple choice worth 1 points) (sinusoidal function context and data modeling mc) when two…

question 7(multiple choice worth 1 points) (sinusoidal function context and data modeling mc) when two species interact in a predator/prey relationship, the population of both species tends to vary with a sinusoidal relationship. one such relationship exists between mice and hawks. the model for the hawk population in a small region is the function predicted f(t)=400 sin(0.8t)+500, where f(t) is the hawk population in month t. what is the approximate value of the predicted value of f(8)?

question 7(multiple choice worth 1 points) (sinusoidal function context and data modeling mc) when two species interact in a predator/prey relationship, the population of both species tends to vary with a sinusoidal relationship. one such relationship exists between mice and hawks. the model for the hawk population in a small region is the function predicted f(t)=400 sin(0.8t)+500, where f(t) is the hawk population in month t. what is the approximate value of the predicted value of f(8)?

Answer

Answer:

  1. First, substitute (t = 8) into the function (f(t)=400\sin(0.8t)+500).
    • We get (f(8)=400\sin(0.8\times8)+500).
    • Calculate (0.8\times8 = 6.4). So, (f(8)=400\sin(6.4)+500).
  2. Then, find the value of (\sin(6.4)).
    • Using a calculator in radian - mode, (\sin(6.4)\approx - 0.587785).
  3. Next, calculate (400\sin(6.4)).
    • (400\times(-0.587785)=-235.114).
  4. Finally, find (f(8)).
    • (f(8)=-235.114 + 500=264.886\approx265).

Explanation:

Step1: Substitute (t = 8)

(f(8)=400\sin(0.8\times8)+500)

Step2: Calculate the argument of sine

(0.8\times8 = 6.4)

Step3: Find sine value

(\sin(6.4)\approx - 0.587785)

Step4: Multiply by 400

(400\times(-0.587785)=-235.114)

Step5: Add 500

(f(8)=-235.114 + 500 = 264.886\approx265)