Write the Word or Phrase That Best Completes Each Statement $$M = 750 + 125 \sin \frac { \pi } { 6 } t$$

question 13

Essay

Write the word or phrase that best completes each statement or answers the question.
-Wildlife management personnel use predator-prey equations to model the populations of certain predators and
their prey in the wild. Suppose the population M of a predator after t months is given by $$M = 750 + 125 \sin \frac { \pi } { 6 } t$$ while the population N of its primary prey is given by $$N = 12,250 + 3050 \cos \frac { \pi } { 6 } t$$ Find the values of $t , 0 \leq t < 12$ , for which the predator population is 875 . Find the values of $t , 0 \leq t < 12$ , for which the prey population is 10,725 .

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Definitions:

Prices

The amount of money required to purchase goods or services, serving as the consideration for the value of the goods or services being exchanged.

Supply and Demand

Supply and demand is a fundamental economic model that explains the interaction between the sellers of a resource and the buyers for that resource, determining its price and quantity in a market.

Allocation of Resources

The process of assigning available resources, or factors of production, to specific uses chosen among many possible and competing alternatives.

Productivity

The assessment of how effectively a person, machine, factory, or system can transform inputs into valuable outputs.