Question

A population of animals oscillates annually from a low of 1300 on January 1st to a high of 2200 on July 1st. and back to a low of 1300 on the following January 1st. Assume that the population is well approximated by a sine or a cosine function.

a. (3 points) State clearly what the period is in terms of months, and then state what the distance between input values for the key points will be.

b. (4 points) Explain how you can determine the midline if you know the minimum and maximum values, and clearly state the midline for this function.

c. (6 points) Explain whether you would choose to use a cosine function or a sine function for this situation, and explain why. Clearly explain if you are using a reflection of one of the basic functions.

d. (12 points) Write the specific function that could be used to model this situation, and then graph the function, clearly marking all key elements on the graph. You DO NOT need to use the entire process we have for graphing a trig function, but can rather use the description of the problem, and your previous answers to create a clearly marked graph. Make sure you clearly label the axes with what they represent in context.

Answer 1