Tire mileage: An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles) A mathematical model for the data is given by f x = − 0.518 x 2 + 33.3 x − 481 (A) Complete the following table. Round values of f x to one decimal place (B) Sketch the graph of f and the mileage data in the same coordinate system . (C) Use the modeling function f x to estimate the mileage for a tire pressure of 31 lbs/sq in . and for 35 lbs/sq in . Round answers to two decimal places. (D) Write a brief description of the relationship between tire pressure and mileage.
Tire mileage: An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles) A mathematical model for the data is given by f x = − 0.518 x 2 + 33.3 x − 481 (A) Complete the following table. Round values of f x to one decimal place (B) Sketch the graph of f and the mileage data in the same coordinate system . (C) Use the modeling function f x to estimate the mileage for a tire pressure of 31 lbs/sq in . and for 35 lbs/sq in . Round answers to two decimal places. (D) Write a brief description of the relationship between tire pressure and mileage.
Tire mileage: An automobile tire manufacturer collected the data in the table relating tire pressure
x
(in pounds per square inch) and mileage (in thousands of miles)
A mathematical model for the data is given by
f
x
=
−
0.518
x
2
+
33.3
x
−
481
(A) Complete the following table. Round values of
f
x
to one decimal place
(B) Sketch the graph of
f
and the mileage data in the same coordinate system.
(C) Use the modeling function
f
x
to estimate the mileage for a tire pressure of
31
lbs/sq
in
.
and for
35
lbs/sq
in
.
Round answers to two decimal places.
(D) Write a brief description of the relationship between tire pressure and mileage.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
The table below shows the numbers of students, in thousands, who have graduated from or are projected to graduate from high school for the years 1996 to 2005.+ (A graphing calculator is recommended.)
Year, x
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Number of students
2540
2633
2740
2786
2820
2837
2886
2929
2935
2944
(in thousands), y
Medicaid The numbers of thousands of peoplecovered by Medicaid for the years 2000–2014 aregiven in the table that follows.
a. Create a scatter plot of the data to determine whattype of function would best model the data.b. Find the equation of the best-fit cubic model.Align the data so that x = 0 is 2000, and roundyour answer to three decimal places.c. Graph the model with the data to see how well themodel fits the data.d. Find a quartic function that models the data,rounded to three decimal places, and graph thisfunction with the data.e. Which function is the better fit for extrapolationafter 2014? Why?
m(c)
C
Write an equation for the function graphed above.
Round to 4 decimal places as needed.
Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
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