Question

The community park has a small lake where visitors can rent paddle boats at $1 for 15 minutes, up to 2 hours. After 2 hours, the rate increases to $3 for 30 minutes.

Problem Write the piecewise function to model this situation and graph the function.

  1. What is the rental charge at 15 minutes? At 16 minutes? At 45 minutes?

2. If you had only $15, how long could you rent a boat?

3. How are the two lines in the graph the same, and how are they different?

4. How would the graph change if the rate change occurred at ? = 1 hour?

5. How would the graph change if the fee were $2 for 15 minutes?

6. What is the rental fee at 3 hours?

Answer 1

The piecewise function to model the situation will be

After 2 hours, the rate increases to $3 for 30 minutes

Hence the piecewise function will be given by

1) Rental charge for 15 minutes = $1

Rental charge for 16 minutes = $2

Rental charge for 45 minutes = $3

2) If we have 15$, then the time we can spend will be given

$8 (For 120 minutes)

$6 (for next 60 minutes)

So, we can have the boat for 180 minutes

3) The two trends lines will increase at constant rate. For the first case (less than 120 minutes), it increases with the slope of 1/15 and then the second case, it increase by a factor of 1/10

4) The second line in the graph will be shifted to the left hand side with the 60 min units

5) The first line graph, slope will be doubled i.e. earlier value was 1/15 and the new value will be 2/15

6) Rental fee for 3 hours will be $14

Note - Post any doubts/queries in comments section.