# The population of an insect species in a stand of trees follows the growth cycle of a tree species.  The insect population is modeled by y = 40 + 30 sin 6t, where t i the number of years since the...

The population of an insect species in a stand of trees follows the growth cycle of a tree species.

The insect population is modeled by y = 40 + 30 sin 6t, where t i the number of years since the stand was first cut in November, 1920.

a) How often does the insect population reach its max level?

b) When did the population last reach its max?

c) What condition in the stand do you think corresponds with the miniumun insect population?

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Given `y=40+30sin6t` where t is the number of years since 1920.

The amplitude of the model is 30 with a midline of 40. Thus the population of insects varies between a maximum of 70 units and a minimum of 10 units.

The period can be found by `p=(2pi)/B` where B is the coefficient of the sine's argument. Thus `p=(2pi)/6=pi/3` . The...

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