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Consider the deer shown above. They are a critical part of the natural food web. They eat small rodents and plants, hence keepingthese populations in check. They are also prey to large animals surnames als such aswolves and coyotes. Their population numbers change over time for many reasons. If the population becomes too large, the deer can cause traffic accidents, bring ticks and disease to local inhabitants, and eat cro and eat crops . For Credit: iStockphoto/Thorsten Spoerlein these reasons, many natural and regulatory conditions cause the populations to rise and fall. Consider the deer shown above. They are a critical part of the natural food web. They eat small rodents and plants, hence keepingthese populations in check. They are also prey to large animals such such aswolves and coyotes . Their population numbers change over time for many reasons. If the population becomes too large, the deer can cause traffic accidents, bring ticks and disease to local inhabitants, and eat crops. For these reasons, many natural and regulatory conditions cause the populations to rise and fall. Natural predator and prey populations can be modeled using a sine or cosine function. For instance, a deer population on a large farm in upstate New York can be modeled using the following formula: Natural predator and prey populations can be modeled using a sine or cosine function. For instance, a deer D(t) = 37 sin( 20t )+253 population on a large farm in upstate New York can be modeled using the following formula: where D(t) predicts the number of deer (in thousands), and t is the number of months since the D(t) = 37 sin ( 20t) + 253 monitoring began. where D(t) predicts the number of deer (in thousands), and t is the number of months since the monitoring began . A third part of the model to analyze is the frequency of the function. In order to understand the model, we begin by analyzing the maximum and minimum values of the Part A: What is the frequency of this function? function and when ( for what values of t) they occur. Frequency: year ( s ) Part A: Given that sin() attains its maximum value when a = ,, explain why the maximum number of deer occur when t = 15 months. Also determine the maximum number of deer. Hint Part B: How does this relate to the original context? Maximum Deer: Edit - Insert- Formats . B I U X X AA- Explanation: Edit - Insert- Formats - B I U X X A A. Question Help: Message instructor Consider the deer shown above. They are a critical part of the natural food web. They eat small rodents and hence keepingthese populations in check. They are also prey to large animals such aswolves and coyotes . Their population numbers change over time for many reasons. If the population becomes too Part B: Given that sin() attains its minimum value when a = 2, show that the minimum large, the deer can cause traffic accidents, bring ticks and disease to local inhabitants, and eat crops. Fo stickS lice the populations to rise and fall. number of deer occur when t = 45 months. Also determine the minimum number of deer. these reasons, many natural and regulatory conditions cause the population Minimum Deer: Natural predator and prey populations can be modeled using a sine or cosine function. For instance, a deer population on a large farm in upstate New York can be modeled using the following formula: Explanation: D(t) = 37 sin(20 t) +253 Edit ~ Insert- Formats - B / U X X' A A - where D(t) predicts the number of deer (in thousands), and t is the number of months since the monitoring began. A second part of the model to analyze is the period of the function. Part A: Decide whether the following statements are true or false. Make sure you know how to correct any that are false. a) One period is indicated by setting the argument of the sine function equal to 27. Select an answer v b) The time between the maximum and minimum values of D(t) is one half of one period. Select an answer v Question Help: Message instructor c) The maximum of the sin function occurs at - of a period. [Select an answer v d) The minimum of the sin function occurs at 7 of a period. [Select an answer Part B: Use any of the true statements above to determine the period of D(t). Period: months Question Help: Message instructor PhotoGrid Calculator