Final answer:
The population of rabbits in July is found by adding the oscillation amplitude of 31 to the average population of 147, resulting in 178 rabbits.
Step-by-step explanation:
The subject of this question is Mathematics, specifically related to sinusoidal functions or harmonic motion often studied in the context of periodic phenomena. The seasonal population changes in rabbits seem to exhibit this kind of oscillation about a mean value. The question states that the population of rabbits is at its lowest in January and oscillates 31 above and below an average of 147 during the year. Considering oscillation in natural populations is often sinusoidal, we can infer that the highest population would occur half a year from January, which is July.
Therefore, to find the population of rabbits in July, one would take the average population and add the amplitude of the oscillation, which is 31: 147 (average) + 31 (above average) = 178. Hence, the correct answer is C. 178.