TOPIC: QUADRATIC APPLICATIONS, PART 1
1. Texas Instruments has found that the revenue produced by selling TI-83 graphing calculators is a function of the price p (dollars per unit) according to the equation:
R(p) = -150 p2 + 21,000p
Domain: ______
Range: ______
a) What should TI charge for each calculator in order to maximize revenue?
b) What is the maximum revenue?
c) What would the revenue be if they decide to charge $100?
d) What other price will yield the same revenue?
2. The cost (C) in number of cents per kilometer of operating a car is a function of the speed (s) in kilometers per hour at which the car is driven. This relationship is represented by the following function:
C = 0.01s2 – s + 37
Domain: ______
Range: ______
a) How much would you spend to drive at 150 km/hr?
b) Between which two speeds must you drive in order to keep your cost to no more than 20 cents per km?
c) What speed should you drive to have the lowest cost per mile?
3. A farmer collected the data below showing crop yields for various amounts of fertilizer.
a) Make a scatter plot of the data.
b) Based on the scatter plot, what type of function would best fit the data?
c) Find the function of best fit. ______
d) Draw the function on the scatter plot.
Domain: ______Range:______
c) How much fertilizer should be applied for maximum yield?
d) What is the maximum yield?
Calculator Steps for the Regression Model
1. Enter the data.
1: Edit…
2. View the scatterplot.
1: Plot 1
Highlight and
Type: Choose Scatterplot
Xlist: L1
Ylist: L2
Set an appropriate window for your data
3. Calculate the model.
Choose the appropriate model.
4. Graph the model.
Clear all equations.
5: Statistics… 1:RegEQ
5. Turn your stat plot off.
4: PlotsOff