Final answer:
The population of mice oscillates around an average with a certain amplitude, and a cosine function is suitable to represent this. The correct equation that models the population P in terms of months since January, given that the amplitude of oscillation is 22 and the average is 121 with a full cycle over 12 months is P = 121 + 22cos(π/6*t), corresponding to Option B.
Step-by-step explanation:
The question asks for an equation to model the population of mice as it oscillates throughout the year. To formulate this model, we take into account the oscillatory nature of the population, mirroring a trigonometric sinusoidal function like sine or cosine. Given that the population is at its lowest in January and oscillates around an average, we can deduce that a cosine function is suitable since the cosine of 0° (or 0 radians) is 1, which would align with the population being at its average, with January being the starting point (t=0).
The amplitude of oscillation is 22 mice, the average population is 121 mice, and since we are dealing in months, and the oscillation occurs over a 12-month period, the horizontal stretch factor of the trigonometric function should correspond to the period of one year. The general formula for the cosine function with a period T is cos(2π/T*t), where t is the time in months. So for a period of 12 months, the wave number (k) needs to be π/6 to get a full oscillation as k = 2π/T = 2π/12 = π/6. Therefore, the equation capturing the population P in terms of months t since January would be P = 121 + 22cos(π/6*t). This makes the correct option from the provided list Option B.