# 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

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: $y=12.000+8.000\mathrm{sin}\left(0.628x\right)$, 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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Velsenw
Given:
The population of a city risen and fallen over a 20-year interval. Its populations may be modeled by the function $y=12000+8000\mathrm{sin}\left(0.628x\right)$, where domain is the year since 1980 and the range is the population of the city.
Calculation:
The given function is $y=12000+8000\mathrm{sin}\left(0.628x\right).$
Comparing, the function with the standard form of the sinusoidal function $y=A\mathrm{sin}\left(Bx-C\right)+D$
$A=8000,B=0.628,C=0,D=12000$
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