## Exam-Style Question on Circular functions## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 55. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is allowed.

The population of sheep on a ranch is modelled by the function \(P(t)= 65 \sin(0.4t-3.2)+450\), where t is in months, and \(t=1\) corresponds to 1st January 2015.

(a) Find the number of sheep on the ranch on 1st July 2015.

(b) Find the rate of change of the sheep population on 1st July 2015.

(c) Explain your answer to part (b) with reference to the sheep population size on 1st July2015.

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