3. What Was the Highest Altitude Reached by the Plane?

Lab 7 Part I

1. A small plane takes off from a regional airport; its altitude at various times is recorded in the table below. Write ordered pairs of the form (Flight time, Altitude) for each pair of values, then plot the points on the graph. Flight Altitudey (feet) Ordered time x(minutes) pair (x, y)

0 0 10 4,000 20 3,000 30 2,000 40 2,000 50 1,000 60 0

2. Connect the points you plotted to draw a graph, and describe what that graph illustrates. Then add a verbal label to each axis that describes the information it represents. 3. What was the highest altitude reached by the plane?

4. How long after the flight began did the plane reach its highest altitude? 5. When was the plane flying level?

6. How long did the flight last?

7. When was the altitude of the plane increasing?

8. When was the altitude of the plane decreasing?

9. Explain why we didn’t bother to include negative values along either axis when drawing the rectangular coordinate system for the altitude graph.

Part II According to taxifarefinder.com, a cab ride from the airport in Las Vegas will cost you an initial charge of $5.10, plus $2.60 per mile. Use this information to fill in the rest of the table describing the total cost for various distances. Then create a scatter diagram (by hand and on minitab), using the distance as x coordinate and the cost as y coordinate.

Distance Cost ($)

0 $5.10

1 $7.70

2 $10.30

5 1. What do you notice about the pattern that the points on your scatter diagram are making? Use that observation about a pattern to connect the points, drawing a graph that represents the cost of a cab ride based on distance. 2. The point where any graph crosses the y axis is called the y- intercept for the graph. Write the coordinates of the y intercept for the graph that you drew. More importantly, what information does the y-intercept represent? 3. How much more will you pay for a 3 mile ride than for a 2 mile ride? 4. How much more will you pay for a 5 mile ride than a 2 mile ride? Explain why that makes sense based on your answer to Question 3. 5. Pick any two points on the graph that you drew, and subtract the second coordinates. Then divide the result by the difference of the first coordinates. What does the result represent about the cab ride? In dividing the difference of the two costs by the difference of the two distances in Question 5, you found the rate of change of the cost as distance changes. When applied to the graph of a line, we call this number, which describes how steep the line is, the slope of the line.

6. The thing that makes a line a line is the fact that the slope never changes. We now know that the slope of a line describes the rate at which the y coordinate changes compared to the x coordinate. Based on this, how can you decide if the relationship between two quantities might be modeled well by a straight line? 7. Estimate the distance of a $16 cab ride. You can use either the table or the graph, but make sure you explain how you got your answer. 8. If x represents the number of miles of a cab ride in Vegas, write an expression that represents the total cost of that ride.

Part III

Everyone knows that after you buy a car, in most cases its value decreases as it gets older. Suppose you bought a used car for $15,000 a few years ago, and its value has been decreasing at the rate of $2,000 per year since then. Make sure you answer each question with a full sentence, with punctuation and everything! Time (yrs) Value ($) 0 $15,000 1 $13,000 2 $11,000 3 $9,000 4 $7,000 5 $5,000

1. Find the y intercept of the graph and explain what it means. (Remember, the y intercept is a point, not a number).

2. Find the slope of the line and explain what it means. In particular, what’s the significance of the sign?

3. Estimate the value of the car after 42 months. (Careful about time units!)

4. Estimate the number of years it took for the car to reach a value of $6,000.

5. If x represents the number of years since the car was bought, write an expression that represents the value of the car.

Part III

We studied the profit made by a small business that sells snow cones. Let’s examine a graph that describes the company’s profit (y) in terms of the number of snow cones sold (x). Again, answer each question with a full sentence.

1. Find the y intercept of the graph and explain what it means. 2. A point where a graph crosses the x axis is called an x intercept of the graph. Find the x intercept of this graph and explain what it means.

3. Find the slope of the line and explain what it means.

4. Estimate the net profit if 150 snow cones are sold. What’s the significance of the sign?

5. Estimate the number of snow cones that need to be sold to make a profit of $50.