일차함수와 그래프

For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in (the referenced table). Assume that the house values are changing linearly.

Year	Indiana	Alabama
1950	$37,700	$27,100
2000	$94,300	$85,100

If we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values will be (or were) equal in what year? (The answer might be absurd.)

In 2004, a school population was 1001. By 2008 the population had grown to 1697. Assume the population is changing linearly.

• ⓐHow much did the population grow between the year 2004 and 2008?
• ⓑHow long did it take the population to grow from 1001 students to 1697 students?
• ⓒWhat is the average population growth per year?
• ⓓWhat was the population in the year 2000?
• ⓔFind an equation for the population, $P,$ of the school t years after 2000.
• ⓕUsing your equation, predict the population of the school in 2011.

In 2003, a town’s population was 1431. By 2007 the population had grown to 2134. Assume the population is changing linearly.

• ⓐHow much did the population grow between the year 2003 and 2007?
• ⓑHow long did it take the population to grow from 1431 people to 2134 people?
• ⓒWhat is the average population growth per year?
• ⓓWhat was the population in the year 2000?
• ⓔFind an equation for the population, $P,$ of the town $t$ years after 2000.
• ⓕUsing your equation, predict the population of the town in 2014.

A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used for voice or video calling. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118.

• ⓐFind a linear equation for the monthly cost of the cell plan as a function of x, the number of monthly minutes used.
• ⓑInterpret the slope and y-intercept of the equation.
• ⓒUse your equation to find the total monthly cost if 687 minutes are used.

A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $10 and then a certain amount of money per megabyte (MB) of data used on the phone. If a customer uses 20 MB, the monthly cost will be $11.20. If the customer uses 130 MB, the monthly cost will be $17.80.

• ⓐFind a linear equation for the monthly cost of the data plan as a function of $x,$ the number of MB used.
• ⓑInterpret the slope and y-intercept of the equation.
• ⓒUse your equation to find the total monthly cost if 250 MB are used.

In 1990, the moose population in a park was measured to be 4,360. By 1999, the population was measured again to be 5,880. Assume the population continues to change linearly.

• ⓐFind a formula for the moose population, P since 1991.
• ⓑWhat does your model predict the moose population to be in 2003?

In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly. Let the input be years since 2003.

• ⓐFind a formula for the owl population, $P.$ Let the input be years since 2003.
• ⓑWhat does your model predict the owl population to be in 2012?

The Federal Helium Reserve held about 16 billion cubic feet of helium in 2010 and is being depleted by about 2.1 billion cubic feet each year.

• ⓐ Give a linear equation for the remaining federal helium reserves, $R,$ in terms of $t,$ the number of years since 2010.
• ⓑ In 2015, what will the helium reserves be?
• ⓒ If the rate of depletion doesn’t change, in what year will the Federal Helium Reserve be depleted?

Suppose the world’s oil reserves in 2014 are 1,820 billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year:

• ⓐ Give a linear equation for the remaining oil reserves, $R,$ in terms of $t,$ the number of years since now.
• ⓑ Seven years from now, what will the oil reserves be?
• ⓒ If the rate at which the reserves are decreasing is constant, when will the world’s oil reserves be depleted?

You are choosing between two different prepaid cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $19.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

You are choosing between two different window washing companies. The first charges $5 per window. The second charges a base fee of $40 plus $3 per window. How many windows would you need to have for the second company to be preferable?

When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $17,000 a year with a commission of 12% of your sales

Option B: Base salary of $20,000 a year with a commission of 5% of your sales

How much jewelry would you need to sell for option A to produce a larger income?

When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $14,000 a year with a commission of 10% of your sales

Option B: Base salary of $19,000 a year with a commission of 4% of your sales

How much electronics would you need to sell for option A to produce a larger income?

When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $20,000 a year with a commission of 12% of your sales

Option B: Base salary of $26,000 a year with a commission of 3% of your sales

How much electronics would you need to sell for option A to produce a larger income?

When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $10,000 a year with a commission of 9% of your sales

Option B: Base salary of $20,000 a year with a commission of 4% of your sales

How much electronics would you need to sell for option A to produce a larger income?

Determine whether the algebraic equation is linear. $2x+3y=7$

Determine whether the algebraic equation is linear. $6{x}^{2}-y=5$

Determine whether the function is increasing or decreasing.

$f(x)=7x-2$

Determine whether the function is increasing or decreasing.

$g(x)=-x+2$

Given each set of information, find a linear equation that satisfies the given conditions, if possible.

Passes through $(7,5)$ and $(3,17)$