Exam 2: Linear Functions and Models

The owner of a gas station records the number of gallons of gas he sells over a period of time. He notices that the number of gallons of gas he sells depends linearly on the price he charges for each gallon. When he charges $1.77 per gallon of gas, he sells 1000 gallons of gas each day. When he charges $2.32 per gallon, he sells 400 gallons. How many gallons of gas would the owner sell if he charged $2.19 per gallon? (Round to the nearest whole number.)

Using the following table of values, determine the average rate of change between and .

After taking a bath you begin to drain the water from the bathtub. The water drains at 0.5 gallon(s) per minute. After 11 minutes, there are 24 gallons of water remaining. How many minutes will it take for the remaining gallons of water to drain from the tub?

The cost of college tuition for 12 credit hours at two local colleges during 2003 to 2008 is shown in the table below. Determine the year that the cost of tuition at School A is expected to be less than the cost of tuition at School B?

The mass of bacteria (in micrograms) in a Petri dish for different times is shown in the table below. Determine the average rate of change of the bacteria from 8:30 am to 10:30 am? (Rounded to the nearest hundredths)

A hotel finds that if it spends no money on renovations, they will be able to rent 135 rooms per night. However, they have found that for every $4000 spent on renovations, they will be able to rent an additional 30 rooms per night. Let x represent the amount of money spent on renovations and y represent the number of rooms rented. Determine a model for the number of rooms rented as a function of the amount of money spent on renovations.

The cost for a cell phone plan at Store A starts at $26.99 per month plus $0.04 per minute. The cost for a cell phone plan at Store B starts at $36.99 per month plus $0.02 per minute. Determine the number of cell phone minutes used for which the monthly cost is the same at both Store A and Store B.

Using the following graph, determine the average rate of change of the function between and .

Biologists observed that as the temperature t (in degrees Fahrenheit) increased near a local ant colony, the speed s that the ants traveled also increased. The data from this observation is shown in the table below. Determine the linear regression equation based on the data provided. (Rounded to the nearest thousandth)

If the slope of a line is m = , then the change in the run is 13.

Find the equation of a line that passes through the points and .

A speed camera records the distance that a car travels along a straight road by taking snapshots of the traveling car at two different times. The first snapshot shows the car is 36 ft away from the speed camera. After half a second, the second snapshot shows the car is 8 ft away from the speed camera. Assume that the car is traveling at a constant speed. a. Based on the speed camera evidence, how fast is the car traveling? b. Find a linear equation that models the car's distance, y , traveled for any amount of time, x . c. How many seconds after the first snapshot does it take for the car to reach the speed camera? d. How far away from the speed camera was the car 1.5 seconds before the first snapshot was taken?

The owner of a gas station records the number of gallons of gas he sells over a period of time. He notices that the number of gallons of gas he sells depends linearly on the price he charges for each gallon. When he charges $1.96 per gallon of gas, he sells 800 gallons of gas each day. When he charges $2.65 per gallon, he sells 400 gallons. Which one of the following graphs illustrate this situation?

Given the graph below, find the rise over run between any two points.

Which one of the following equations has a graph that is parallel to the line shown in the graph below?

Using the following table of values, determine the average rate of change between and .

Find the equation of the line for the following graph.

Using the graph below, determine the point where the graphs intersect.

Find the slope and y -intercept for the equation .

Using the function , determine the average rate of change of the function between and .