Question

I REALLY NEED HELP!!!!!!!

The table below represents the velocity of a car as a function of time.
Table:
Time Velocity
(hour) (miles/hour)
x y
0 50
1 52
2 54
3 56
Part 1: What is the y-intercept of the function, and what does this tell you about the car?
Part 2: Calculate the average rate of change of the functino represented by the table between x=1 to x=3 hours, and what does the average rate represent?
Part 3: What would be the domain of the function if the velocity of the car was measured until it reached 60 miles/hour and the car does not change motion?1

Answer 1

We plot these data where x corresponds to the time and y corresponds to the velocity. Using the calculator, y - intercept is equal to 50. y-intercept is the y-value when x is zero. The car is accelerating. The average rate of change when x =1 to x=3 is (56-52)/(3-1) or 2 miles/hour^2. The car would reach 60 miles/hour when x=5 from the acceleration of 2. Domain is 5.

Hope this helps :)

Answer 2

Part 1

The y-intercept is found in the table by looking for the entry where x=0. That is y=50.

Part 2

The average rate of change is the amount of change divided by the width of the interval. From x=1 to 3, that is

... average rate of change = (56 mph - 52 mph)/(3 h - 1 h) = 4/2 mph/h = 2 mph/h

The rate of change in velocity is acceleration. This represents the average acceleration of the car.

Part 3

From the last table entry to 60 mph, the car must increase in speed by 4 mph. We know from part 2 that this change takes 2 hours to accomplish. Adding 2 hours to the last entry in the table brings the x-value to 5. The domain of the function would need to be increased to cover the interval [0, 5] hours.