Short Answer

Question

A dvd store charges $4.70 for each day, d, a dvd is rented. The store also gives you a dollar off if the dvd is returned before 5 days.

a. write a rule to represent the rental charges C

b. How much will you pay if you return the dvd after 4 days? 7 days?

Answer 1

Hi Hailey,

 

The rule to represent the rental charges (C) based upon the number of days (d) is an example of what is called a piece-wise function, i.e. multiple output rules based upon different input conditions.

 

Here then is our rule to determine the output rental charges (C) based upon the value of the input days (d):

    1 ≤ d ≤ 4 | C = 4.70d - 1.00

          d ≥ 5 | C = 4.70d

 

Next, we'll use the appropriate rule in each case to determine the rental charges (C) for days rented (d):

    4-day rental:  

        C = 4.70(d) - 1.00

        C = 4.70(4) - 1.00

        C = 18.80 - 1.00

        C = $17.80

    7-day rental:

        C = 4.70(d)

        C = 4.70(7)

        C = $32.90

 

Below is the link to our graph of this piece-wise function:

 

https://dl.dropbox.com/s/bfah0sbsbvcweue/Graph_of_Piecewise_DVD_Rental_Function.png?raw=1

 

As can be seen, the appropriate output rule for rental charges

(y dollars) was used based upon the value of the input number of days (x).  The blue line shows the graph for shorter rentals (4 days or less) and the green line shows the rule for longer rentals (5 days or more).  The 4-day rental charge of $17.80 is appropriately shown on the blue line and 7-day rental charge of $32.90 is appropriately shown on the green line.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.