5.In a certain state the maximum speed permitted on freeways is 65 km/h and the minimum speed is 40 km/h. The fine for violating these limits is Rs.15 for every kilometer per hour above the maximum speed or below the minimum speed. Express the amount of the fine as a function of the driving speed and graph for 100.
f(s) =
15(s-65) for s>65
15(40-s) for s<45
or
f(s) = 15|s-52.5| if |s-52.5| > 12.5
f(s) = 0 otherwise.
To express the amount of the fine as a function of the driving speed, we can define the fine function as follows:
Let x represent the driving speed in km/h.
If the driving speed is above the maximum speed of 65 km/h, the fine will be Rs.15 multiplied by the number of km/h above 65, which can be expressed as:
Fine(x) = 15(x - 65), for x > 65
If the driving speed is below the minimum speed of 40 km/h, the fine will be Rs.15 multiplied by the number of km/h below 40, but since the minimum fine limit is 0, we can set the fine to 0 in this case:
Fine(x) = 0, for x < 40
If the driving speed is between 40 km/h and 65 km/h (inclusive), there are no fines as the driver is within the speed limits:
Fine(x) = 0, for 40 <= x <= 65
To graph the fine function for x = 100:
Given that 100 is above the maximum speed of 65 km/h, we can calculate the fine using the formula for speeds above the maximum:
Fine(100) = 15(100 - 65) = 15(35) = Rs.525
Therefore, the amount of the fine for a driving speed of 100 km/h is Rs.525.