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Explain how to find the input variable in a word problem that uses a linear function.
Determine the independent variable. This is the variable upon which the output depends.
Explain how to find the output variable in a word problem that uses a linear function.
Explain how to interpret the initial value in a word problem that uses a linear function.
To determine the initial value, find the output when the input is equal to zero.
Explain how to determine the slope in a word problem that uses a linear function.
Find the area of a parallelogram bounded by the y -axis, the line $\text{\hspace{0.17em}}x=3,$ the line $\text{\hspace{0.17em}}f(x)=1+2x,$ and the line parallel to $\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ passing through $\text{\hspace{0.17em}}\left(\text{2},\text{7}\right).$
6 square units
Find the area of a triangle bounded by the x -axis, the line $\text{\hspace{0.17em}}f(x)=12\u2013\frac{1}{3}x,$ and the line perpendicular to $\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ that passes through the origin.
Find the area of a triangle bounded by the y -axis, the line $\text{\hspace{0.17em}}f(x)=9\u2013\frac{6}{7}x,$ and the line perpendicular to $\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ that passes through the origin.
20.01 square units
Find the area of a parallelogram bounded by the x -axis, the line $\text{\hspace{0.17em}}g(x)=2,$ the line $\text{\hspace{0.17em}}f(x)=3x,$ and the line parallel to $\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ passing through $\text{\hspace{0.17em}}(6,1).$
For the following exercises, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped 4,700. Assume this trend continues.
Identify the year in which the population will reach 0.
For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues.
Identify the year in which the population will reach 75,000.
For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.
Find the linear function that models the town’s population $\text{\hspace{0.17em}}P\text{\hspace{0.17em}}$ as a function of the year, $\text{\hspace{0.17em}}t,$ where $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ is the number of years since the model began.
$P\left(t\right)=75,000+2500t$
Find a reasonable domain and range for the function $\text{\hspace{0.17em}}P.$
If the function $\text{\hspace{0.17em}}P\text{\hspace{0.17em}}$ is graphed, find and interpret the x - and y -intercepts.
(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.
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