Automobile production. The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market. A mathematical model for this data is given by f x = − 0.0169 x 2 + 0.47 x + 17.1 where x = 0 corresponds to 1980. (A) Complete the following table. Round values of f x to one decimal place. (B) Sketch the graph of f and the market share data in the same coordinate system . (C) Use values of the modeling function f to estimate Ford’s market share in 2020 and in 2025. (D) Write a brief verbal description of Ford’s market share from 1980 to 2010.
Automobile production. The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market. A mathematical model for this data is given by f x = − 0.0169 x 2 + 0.47 x + 17.1 where x = 0 corresponds to 1980. (A) Complete the following table. Round values of f x to one decimal place. (B) Sketch the graph of f and the market share data in the same coordinate system . (C) Use values of the modeling function f to estimate Ford’s market share in 2020 and in 2025. (D) Write a brief verbal description of Ford’s market share from 1980 to 2010.
Solution Summary: The author calculates the value of f(x) to one decimal place in the table shown below for the values of x.
Automobile production. The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market.
A mathematical model for this data is given by
f
x
=
−
0.0169
x
2
+
0.47
x
+
17.1
where
x
=
0
corresponds to 1980.
(A) Complete the following table. Round values of
f
x
to one decimal place.
(B) Sketch the graph of
f
and the market share data in the same coordinate system.
(C) Use values of the modeling function
f
to estimate Ford’s market share in 2020 and in 2025.
(D) Write a brief verbal description of Ford’s market share from 1980 to 2010.
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.
Temperature measurements are based on the transfer of heat between the sensor of a measuring device (such as an ordinary thermometer or the gasket of a thermocouple) and the medium whose temperature is to be measured. Once the sensor or thermometer is brought into contact with the medium, the sensor quickly receives (or loses, if warmer) heat and reaches thermal equilibrium with the medium. At that point the medium and the sensor are at the same temperature. The time required for thermal equilibrium to be established can vary from a fraction of a second to several minutes. Due to its small size and high conductivity it can be assumed that the sensor is at a uniform temperature at all times, and Newton's cooling law is applicable. Thermocouples are commonly used to measure the temperature of gas streams. The characteristics of the thermocouple junction and the gas stream are such that λ = hA/mc 0.02s-1. Initially, the thermocouple junction is at a temperature Ti and the gas stream at…
A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?
Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
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