2. The population of a ski-resort town, as a function of the number of months into the year, can be described by a sinusoidal function. The maximum population of the town is about 15 000 people, and the minimum population is about 500 people. At the beginning of the year, the population is at its greatest. After six months, the population reaches its lowest number of people. A) Sketch 1 cycle of this scenario, showing the population in terms of months. (***Note: Remember to label the 5 main coordinates of each cycle, and the equation of axis.***) B) Develop a positive sine expression (in terms of radians) that models the sketch, and explain how you determined each part of the equation. C) Imagine the maximum population of the town decreases to 12,500 people, and it takes only 3 months for the town to reach the same minimum population. Explain/calculate the changes to the equation, and write the new equation.
2. The population of a ski-resort town, as a function of the number of months into the year, can be described by a sinusoidal function. The maximum population of the town is about 15 000 people, and the minimum population is about 500 people. At the beginning of the year, the population is at its greatest. After six months, the population reaches its lowest number of people. A) Sketch 1 cycle of this scenario, showing the population in terms of months. (***Note: Remember to label the 5 main coordinates of each cycle, and the equation of axis.***) B) Develop a positive sine expression (in terms of radians) that models the sketch, and explain how you determined each part of the equation. C) Imagine the maximum population of the town decreases to 12,500 people, and it takes only 3 months for the town to reach the same minimum population. Explain/calculate the changes to the equation, and write the new equation.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Transcribed Image Text:2. The population of a ski-resort town, as a function of the number of
months into the year, can be described by a sinusoidal function. The
maximum population of the town is about 15 000 people, and the
minimum population is about 500 people. At the beginning of the year,
the population is at its greatest. After six months, the population reaches
its lowest number of people.
A) Sketch 1 cycle of this scenario, showing the population in terms of
months.
(***Note: Remember to label the 5 main coordinates of each cycle, and
the equation of axis.***)
B) Develop a positive sine expression (in terms of radians) that models
the sketch, and explain how you determined each part of the equation.
C) Imagine the maximum population of the town decreases to 12,500
people, and it takes only 3 months for the town to reach the same
minimum population. Explain/calculate the changes to the equation,
and write the new equation.
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