Math

Math Genius:

The population in a region varies with the number of preditors at any time, you could predict the rodent population r(t)=2500+1500sin(Pi/4*t) where t is the number of years since 1976, verify that the year 1982 was a year of minimum

Hi Math Genius,
I have assumed that the by pi/4*t you meant pi*t / 4
I don't want to actually do it for you but I am happy to help you along the way.
It is a differentiation question.
Stationary points are when the gradient of the tangent to the curve = 0 (that is dr/dt = 0)
The stationary point will be a minimum if the curve is concave up at that point. (that is d ²r/dt ² > 0)

t = 0 in 1976, so what t do you care about?

Is that enough to get you started? If you want more help show me what you have done to help yourself first.