The equation and graph show the distance traveled by a convertible and a limousine in miles, y, as a
function of time in hours, .
Convertible:
y = 35z
Compare the rates of change of the
two vehicles.
The rate of change of the limousine is
?
the rate of change
of the convertible.
Distance (mi)
904
80
70
60
50
40
Limousine
30
20
10
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Time (hr)
The rate of change of the limousine is 35 miles per hour, which is the same as the rate of change of the convertible.
To compare the rates of change of the two vehicles, we need to find the rate of change for each vehicle. The rate of change, or slope, can be calculated by finding the difference in distance (y) and the difference in time (z) between two points on the graph.
From the given information, we have a table with the distance (y) traveled by the limousine at different times (z).
Distance (mi) | Time (hours)
904 | 0
80 | 1
70 | 2
60 | 3
50 | 4
40 | 5
To find the rate of change for the limousine, we can calculate the difference in distance (y) divided by the difference in time (z) between two consecutive time points.
Rate of change of the limousine = (Change in distance) / (Change in time)
For example, to find the rate of change between the first two time points (0 hour and 1 hour):
Rate of change = (80 - 904) / (1 - 0) = (-824) / 1 = -824 miles per hour
Similarly, we can calculate the rate of change for the other time intervals.
Rate of change between 1 hour and 2 hours = (70 - 80) / (2 - 1) = -10 miles per hour
Rate of change between 2 hours and 3 hours = (60 - 70) / (3 - 2) = -10 miles per hour
Rate of change between 3 hours and 4 hours = (50 - 60) / (4 - 3) = -10 miles per hour
Rate of change between 4 hours and 5 hours = (40 - 50) / (5 - 4) = -10 miles per hour
From these calculations, we can see that the rate of change of the limousine is constant at -10 miles per hour.