Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and m x represents the gas mileage (in mpg). a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the neatest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and m x represents the gas mileage (in mpg). a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the neatest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.
Solution Summary: The author explains how to determine the quadratic function of the following data using Ti-83 graphing calculator.
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and
m
x
represents the gas mileage (in mpg).
a. Use regression to find a quadratic function to model the data.
b. At what speed is the gas mileage the greatest? Round to the neatest mile per hour.
c. What is the maximum gas mileage? Round to the nearest mile per gallon.
Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
(c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to
increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with
corresponding ordered pairs and label the asymptote with its equation. Write the domain and range of the function
in interval notation. Make your graph big enough to see all important features.
Find the average value gave of the function g on the given interval.
gave =
g(x) = 8√√x, [8,64]
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