Question

analyzing the trip
mayra said: the flight felt fast, but the trip felt slow
a select two points on the graph. calculate the
average rate of change for the interval you selected
b. can you find:
. mayras average rate of change for the full trip?
. mayras average rate of change during the flight?

Explanation:

Step1: Calculate average rate of change for interval \(0.5\) to \(2.5\) hours

The formula for average rate of change is \(\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1 = 0.5,y_1=20,x_2 = 2.5,y_2 = 20\).
So, \(\frac{20 - 20}{2.5 - 0.5}=\frac{0}{2}=0\)

Step2: Calculate average rate of change for full trip

Assume the final time \(x_f\) (say \(x_f = 5\) hours) and final distance \(y_f=420\) miles (approx from graph). Initial point \((x_i = 0,y_i = 0)\)
Average rate of change \(\frac{y_f - y_i}{x_f - x_i}=\frac{420-0}{5 - 0}=84\) miles per hour

Step3: Calculate average rate of change during flight

Assume flight interval: from \(x_1 = 2.5\) to \(x_2=4\) (approx). Let \(y_1 = 20,y_2 = 400\) (approx from graph)
Average rate of change \(\frac{400 - 20}{4 - 2.5}=\frac{380}{1.5}=\frac{760}{3}\approx253.33\) miles per hour

Answer:

a. For the interval \(0.5\) to \(2.5\) hours, the average rate of change is \(0\) miles per hour.
b.

• Mayra's average rate of change for the full trip (assuming final time \(5\) hours and final distance \(420\) miles) is \(84\) miles per hour.
• Mayra's average rate of change during the flight (assuming flight interval \(2.5 - 4\) hours and distance change \(20 - 400\) miles) is approximately \(253.33\) miles per hour.