# Applied Linear Functions: A Question of Cost

To print: Linear Relations 4 applications

# Appliance Repair

Here is a set of points showing the relationship between how long an appliance repair technician works in a home and how much their visit costs.

(a) How much does it cost to have the technician arrive at your house?

(b) How much does the fee increase for each hour?

A rate of change is the increase of the dependent variable (vertical increment) for every one unit of increase of the independent (horizontal increment) variable.

(c) Copy and complete: The rate of change is …… dollars for one hour.

The function that maps the number of hours to the cost can be written as

(d)    Type this function in to the applet above.

(e)   Using the function, calculate the value when ?

(f)   The appliance repair technician works for 1 hour and 55 minutes. How much does their time cost?

(g)  At a different house, they charge 150 dollars. For how long did they work?

# Truck Rental

Here is a set of points showing the relationship between the how far a cargo truck is driven and how much it costs to rent it.

(a) How much does it cost to rent the truck and to not drive it anywhere?

(b) How much does the price increase every 10 km driven?

(c) How much does the price increase for every 1 km driven?

(d) Complete: The rate of change is cost is ….. dollars for every one km driven.

(e) The function maps the value km to the value cost.

What are and in this formula?

Try your equation out in the applet above.

(f) Use your function to calculate the cost when the number of kilometers driven .

(g) Use your function to calculate the number of kilometers driven when the cost .

# Town Hall Rental

Here is a set of points representing how much it costs to rent a town hall for a private function. To rent the hall, you pay a set fee for cleaning and then you pay for the number of hours you use the hall. The hourly rate is reduced the longer you rent the hall.

(a)       How much does it cost to rent the hall for 2 hours?

(b)      What is the set cleaning fee?

(c)       What is the hourly rate, for the first four hours?

(d)      What is the hourly rate for hours 4 to 8?

(e)       Complete the following three functions:

(f)       Type each function in to the applet above. Use 0<=h<=4 for the first domain, etc.

# Electricity Bill

An electricity bill (BC, Canada, April 2018) for a 30 day period is made up of three components, before tax

1. A fixed cost of services such as billing etc, dollars total for 30 days.
2. dollars per kilowatt up to 660 kilowatts
3. dollars per kilowatt for any kilowatts over 660.

(a) Calculate the following costs and plot the points:

 KWatts 0 200 400 600 660 800 1000 Cost

Type them in with uppercase letters, such as etc.

(b) Complete the following two functions:

(c) Type in your functions to see if they match the points that you plotted.