5. The population of a deer herd varies sinusoidally with a period of one year. The population is at a minimum at the beginning of the year when the population is about 4000 animals. The population is at a maximum of 6000 animals after 6 months which is at the end of June or the beginning of July. a) Without graphing, determine a sine or cosine function to the number of animals. Let N represent the number of animals and let t represent the number of months elapsed. b) How many animals are there expected to be at the end of the 7th month? Round your answer to one decimal place. c) Determine algebraically when there will be 4500 animals. Show your work.

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