일차함수와 그래프

The number of people afflicted with the common cold in the winter months dropped steadily by 50 each year since 2004 until 2010. In 2004, 875 people were inflicted.

Find the linear function that models the number of people afflicted with the common cold C as a function of the year, $t.$ When will no one be afflicted?

For the following exercises, use the graph in (the referenced figure) showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$10,000 and ending at 2005 at$4,000. The x-axis ranges from 0 to 30 in intervals of 5 and the y –axis goes from 0 to 12,000 in intervals of 2,000." loading="lazy" decoding="async">

Find the linear function y, where y depends on $x,$ the number of years since 1980.

For the following exercises, use the graph in (the referenced figure) showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$10,000 and ending at 2005 at$4,000. The x-axis ranges from 0 to 30 in intervals of 5 and the y –axis goes from 0 to 12,000 in intervals of 2,000." loading="lazy" decoding="async">

Find and interpret the y-intercept.

For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500.

Assume the population is changing linearly.

• ⓐHow much did the population grow between the year 2004 and 2012?
• ⓑWhat is the average population growth per year?
• ⓒFind an equation for the population, P, of the school t years after 2004.

For the following exercises, consider this scenario: In 2000, the moose population in a park was measured to be 6,500. By 2010, the population was measured to be 12,500. Assume the population continues to change linearly.

Find a formula for the moose population, $P$.

For the following exercises, consider this scenario: In 2000, the moose population in a park was measured to be 6,500. By 2010, the population was measured to be 12,500. Assume the population continues to change linearly.

What does your model predict the moose population to be in 2020?

For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in (the referenced table). Assume that the house values are changing linearly.

Year	Pima Central	East Valley
1970	32,000	120,250
2010	85,000	150,000

In which subdivision have home values increased at a higher rate?

For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in (the referenced table). Assume that the house values are changing linearly.

Year	Pima Central	East Valley
1970	32,000	120,250
2010	85,000	150,000

If these trends were to continue, what would be the median home value in Pima Central in 2015?

Terry is skiing down a steep hill. Terry's elevation, $E(t),$ in feet after $t$ seconds is given by $E(t)=3000-70t.$ Write a complete sentence describing Terry’s starting elevation and how it is changing over time.

Maria is climbing a mountain. Maria's elevation, $E(t),$ in feet after $t$ minutes is given by $E(t)=1200+40t.$ Write a complete sentence describing Maria’s starting elevation and how it is changing over time.

Jessica is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate in miles per hour?

Sonya is currently 10 miles from home and is walking farther away at 2 miles per hour. Write an equation for her distance from home t hours from now.

A boat is 100 miles away from the marina, sailing directly toward it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.

Timmy goes to the fair with $40. Each ride costs $2. How much money will he have left after riding $n$ rides?

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$y=\frac{1}{4}x+6$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$y=3x-5$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$y=3{x}^{2}-2$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$3x+5y=15$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$3{x}^{2}+5y=15$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$3x+5{y}^{2}=15$