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# For the following exercises, use this scenario: The population of a city has risen and fallen over a 20-year interval. Its population maybe modeled by the following function: y = 12.000 + 8.000 sin(0.628x), where the domain is the years since 1980 and the range is the population of the city. Graph the function on the domain of [0,40]

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Comparing two groups
asked 2021-02-20
For the following exercises, use this scenario: The population of a city has risen and fallen over a 20-year interval. Its population maybe modeled by the following function: $$y = 12.000 + 8.000 \sin(0.628x)$$, where the domain is the years since 1980 and the range is the population of the city.
Graph the function on the domain of [0,40]

## Answers (1)

2021-02-21
Given:
The population of a city risen and fallen over a 20-year interval. Its populations may be modeled by the function $$y = 12000 + 8000 \sin (0.628x)$$, where domain is the year since 1980 and the range is the population of the city.
Calculation:
The given function is $$y = 12000 + 8000 \sin (0.628x).$$
Comparing, the function with the standard form of the sinusoidal function $$y = A \sin (Bx - C) + D$$
$$A = 8000, B = 0.628, C = 0, D = 12000$$
The amplitude is $$A = 8000$$
The periodis given by
$$\frac{2 \pi}{B}$$
$$\frac{2 \pi}{0.628}= \frac{3.14}{0.314}$$
$$= 10$$
And the phase shift is $$C = 0$$
Using these properties, the graph of the function in the domain [0,40] has been shown below

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