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Choosing a Window Use a graphing calculator or computer to decide which viewing rectangle (a)—(d) produces the most appropriate graph of the equation.
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- Baking a Potato: A potato is placed in a preheated oven to bake. Its temperature P=P(t) is given by P=400325et/50, Where P is measured in degrees Fahrenheit and t is the time in minutes since the potato was placed in the oven. a. Make a graph of P versus t.Suggestion: in choosing your graphing window, it is reasonable to look at the potato over no more than a 2-hour period. After that, it will surely be burned to a crisp. You may wish to look at a table of values to select a vertical span. b. What was the initial temperature of the potato? c. Did the potatos temperature rise more during the first 30 minutes or second 30 minutes of baking? What was the average rate of change per minute during the first 30 minutes? What was the average rate of change per minute during the second 30 minutes. d. Is this graph concave up or concave down? Explain what that tells you about how the potato heats up, and relate this to part c.. e. The potato will be done when it reaches a temperature of 270 degrees. Approximate the time when the potato will be done. f. What is the temperature of the oven? Explain how you got your answer. Hint: if the potato were left in the oven for a long time, its temperature would match that of the oven.arrow_forwardMeasurement Use the fact that 13 inches is approximately the same length as 33 centimeters to find a mathematical model that relates centimeters y to inches x. Then use the model to find the numbers of centimeters in 10 inches and 20 inches.arrow_forwardThink About It Find a and b when the graph of y=ax2+bx3 is symmetric with respect to (a) the y -axis and (b) the origin. (There are many correct answers.)arrow_forward
- Temperature The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where x = 0 corresponds to 6 a.m. These data can be approximated by the model y=0.026x31.03x2+10.2x+34,0x24 Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. How well does the model fit the data? Use the graph to approximate the times when the temperature was increasing and decreasing. Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?arrow_forwardDiscuss Enter Equations carefully A student wishes to graph the equations y=x1/3 and y=xx+4 On the same screen, so he enters the following information into his calculator: y1=X1/3y2=X/X+4 The calculators graph two lines instead of the equations he wanted. What went wrong?arrow_forwardMeasurement Use the fact that 14 gallons is approximately the same amount as 53 liters to find a mathematical model that relates liters y to gallons x. Then use the model to find the numbers of liters in 5 gallons and 25 gallons.arrow_forward
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