Some populations of animals exhibit periodic behavior over time. During the 1960s and 1970s, two scientists carefully studied the population of the Carabid beetle in a region of the Netherlands. Assume that the table below shows the results from their study. Without the aid of technology, choose the sine model which is the most reasonable fit to data, where x is the number of years since 1964.

Question

Quizplus · Accepted Answer

Looking at the data, we see a clear repeating pattern occurring every 4 years. This indicates a period of 4 for the sine model. 
We can then estimate the amplitude to be approximately 75 (average of the high and low values) and a vertical shift of approximately 250. 
Using this information, we can eliminate choices A and B, which have periods of 2 and 1 respectively, and choices D and E, which have amplitudes that are far too large compared to the data. 
The remaining choice, C, has a period of 4 and an amplitude and vertical shift that are consistent with the data. Thus, choice C is the most reasonable fit.

Some Populations of Animals Exhibit Periodic Behavior Over Time