Given: P(0) = 950. P(t) measures the # of rabbits in the rabbit population at an unspecified location. t measures time, with t measured in units of 1 month (not precise). The population of rabbits oscillates with a period of 1 year, but the type of periodic oscillation as a function of time is not given. I will assume a negative cosine curve with a baseline average of 19 rabbits and an amplitude of 19 rabbits, which has a minimum of 0 rabbits in January and a maximum of 38 rabbits in July. We are also told the rabbiit population increases by 180 each year without being told if this is a linear increase each month or not. I will assume it is a linear increase of 15 rabbits per month. With these interpretations for the statement of the problem, we can answer the question:
P(t) = 950 + 19-19 cos((2π/12)(t-1)) + 15t
Note: At time t=7, which is July, the rabbit population is at a maximum because -19 cos((2π/12)(7-1)) = -19 cos(π) = +19.
