QuestionQuestion The equation $p=7000 \cos \left(\frac{\pi}{10} t\right)+45000$ describes the number of deer in a forest where $t$ is the number of years after 1972. What was the population in the year 1978 to the nearest whole number? NOTE: The angle is in radians.
Provide your answer below: $$p=\square]^{\text {deer }}$$

Studdy Solution
Calculate the population $p$:
First, calculate the angle: $$\frac{\pi}{10} \times 6 = \frac{6\pi}{10} = \frac{3\pi}{5}$$
Next, calculate $\cos\left(\frac{3\pi}{5}\right)$. Using a calculator, we find: $$\cos\left(\frac{3\pi}{5}\right) \approx -0.809$$
Substitute this value back into the equation: $$p = 7000 \times (-0.809) + 45000$$ $$p \approx -5663 + 45000$$ $$p \approx 39337$$
Round to the nearest whole number: $$p = 39337$$
The population in the year 1978 was:
$$p = \boxed{39337} \text{ deer}$$