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college mathematics for business

Questions and Answers of College Mathematics For Business

In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.Every rational function is a polynomial function.
Marine life depends on the microscopic plant life that exists in the photic zone, a zone that goes to a depth where only 1% of surface light remains. In some waters with a great deal of sediment, the
In Problem find and simplify the expression if f(x) = x2 - 4.f(x - 1)
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 byf(x) = -0.0117x2 + 0.32x + 17.9where
Using quadratic regression on a graphing calculator, show that the quadratic function that best fits the data on tire mileage in Problem 65 isf(x) = -0.518x2 + 33.3x - 481Problem 65An automobile tire
For Problem solve each equation to four decimal places.10x = 12
In 2015, the estimated population of South Sudan was 12 million with a relative growth rate of 4.02%.(A) Write an equation that models the population growth in South Sudan, letting 2015 be year 0.(B)
In Problem find and simplify the expression if f(x) = x2 - 4.f(x3)
Table 5 shows the marriage and divorce rates per 1,000 population for selected years since 1960.(A) Let x represent the number of years since 1960 and find a cubic regression polynomial for the
In 2015, the estimated population of Brazil was 204 million with a relative growth rate of 0.77%.(A) Write an equation that models the population growth in Brazil, letting 2015 be year 0.(B) Based on
In Problem find and simplify the expression if f(x) = x2 - 4.f(√x)
Using quadratic regression on a graphing calculator, show that the quadratic function that best fits the data on market share in Problem 66 isf(x) = -0.0117x2 + 0.32x + 17.9Problem 66The table shows
The manufacturer of the bicycle helmets in Problem 67 is willing to supply x helmets at a price of p(x) as given by the equationp(x) = 4√x 9 ≤ x ≤ 289(A) Describe how the graph of
Refer to Table 5.(A) Let x represent the number of years since 1960 and find a cubic regression polynomial for the divorce rate.(B) Use the polynomial model from part (A) to estimate the divorce rate
For Problem solve each equation to four decimal places.ex = 4.304
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.There exists a rational function that has both a vertical and horizontal
Using statistical methods, the financial department of a hospital arrived at the cost equationC(x) = 0.00048(x - 500)3 + 60,000 100 ≤ x ≤ 1,000where C(x) is the cost in dollars for
In 2015, the estimated population of Japan was 127 million with a relative growth rate of -0.16%.(A) Write an equation that models the population growth in Japan, letting 2015 be year 0.(B) Based on
In Problem find and simplify the expression if f(x) = x2 - 4.f(4√ x)
Write an equation for the graph shown in the form y = a(x - h)2 + k, where a is either -1 or +1 and h and k are integers. -5 -5
The marketing research department for a company that manufactures and sells memory chips for microcomputers established the following price–demand and revenue functions:p(x) = 75 - 3x
For Problem solve each equation to four decimal places.1.00512t = 3
In Problem find and simplify the expression if f(x) = x2 - 4.f(-3) + f(h)
For Problem solve each equation to four decimal places.1.024t = 2
Use the revenue function from Problem 69 and the given cost function:R(x) = x(75 - 3x) Revenue functionC(x) = 125 + 16x Cost functionwhere x is in millions of chips, and
Graph Problem using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals.y = ln x
Table 5 shows state income tax rates for married couples filing a joint return in Louisiana.(A) Write a piecewise definition for T(x), the tax due on a taxable income of x dollars.(B) Graph T(x).(C)
In Problem find and simplify the expression if f(x) = x2 - 4.f(2 + h) - f(2)
In Problem find and simplify the expression if f(x) = x2 - 4.f(-3 + h)
Use the revenue and cost functions from Problem 71:R(x) = x(75 - 3x) Revenue functionC(x) = 125 + 16x Cost functionwhere x is in millions of chips, and R(x) and C(x) are in millions of dollars. Both
Graph Problem using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals.y = |ln x|
In Problem find and simplify the expression if f(x) = x2 - 4.f(-3 + h) - f(-3)
Table 6 shows state income tax rates for individuals filing a return in Louisiana.(A) Write a piecewise definition for T(x), the tax due on a taxable income of x dollars.(B) Graph T(x).(C) Find the
The French physician Poiseuille was the first to discover that blood flows faster near the center of an artery than near the edge. Experimental evidence has shown that the rate of flow v (in
In Problem find and simplify each of the following, assuming h ≠ 0 in (C).f(x) = 4x - 3 (A) f(x + h) (B) f(x + h) - f(x) f(x + h) - f(x) (C) h
Solve Problem exactly without using a calculator.log x - log 3 = log 4 - log(x + 4)
In Problem(A) Graph f and g in the same coordinate system.(B) Solve f(x) = g(x) algebraically to two decimal places.(C) Solve f(x) > g(x) using parts (A) and (B).(D) Solve f(x) < g(x) using
BanxQuote operates a network of websites providing real-time market data from leading financial providers. The following rates for 12-month certificates of deposit were taken from the websites:(A)
In Problem find and simplify the expression if f(x) = x2 - 4.f(x + 2)
Table 5 shows estimates of mobile data traffic, in exabytes (1018 bytes) per month, for years from 2015 to 2020.(A) Let x represent the number of years since 2015 and find an exponential regression
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.Every polynomial function is a rational function.
In Problem does the equation specify a function with independent variable x? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y.y(x
Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. f(x) -5 5
Table 4 shows the number of individuals worldwide who could access the internet from home for selected years since 2000.(A) Let x represent the number of years since 2000 and find an exponential
In Problem find the equations of any vertical asymptotes. x? + 3x f(x) x + 2x
A consulting firm, using statistical methods, provided a veterinary clinic with the cost equationC(x) = 0.00048(x - 500)3 + 60,000100 ≤ x ≤ 1,000where C(x) is the cost in dollars for handling x
In Problem find the equations of any vertical asymptotes. f(x) x + 100 x 100
How can you tell from the vertex form y = a(x - h)2 + k whether a quadratic function has no real zeros?
How can you tell from the standard form y = ax2 + bx + c whether a quadratic function has exactly one real zero?
How can you tell from the graph of a quadratic function whether it has exactly one real zero?
In Problem find the equation of any horizontal asymptote. 5х + 4 х? — Зх + 1 f(x)
In Problem does the equation specify a function with independent variable x? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y.√x
A company is trying to introduce a new product to as many people as possible through television advertising in a large metropolitan area with 2 million possible viewers. A model for the number of
An office copier has an initial price of $2,500. A service contract costs $200 for the first year and increases $50 per year thereafter. It can be shown that the total cost of the copier after n
In Problem find the equation of any horizontal asymptote. x? + 4 f(x) 100x + 1
How can you tell from the standard form y = ax2 + bx + c whether a quadratic function has two real zeros?
In Problem find the equation of any horizontal asymptote. 3x + 2x – 1 4x2 - f(x) 5x + 3
In Problem does the equation specify a function with independent variable x? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y.x3 -
How can you tell from the graph of a quadratic function whether it has no real zeros?
In Problem does the equation specify a function with independent variable x? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y.x2 +
Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. f(x) -5
Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. f(x) -5 5 -5
In Problem(A) Graph f and g in the same coordinate system.(B) Solve f(x) = g(x) algebraically to two decimal places.(C) Solve f(x) > g(x) using parts (A) and (B).(D) Solve f(x) < g(x) using
Let f(x) = x2 - 3x + 1. Find (A) f(a) (B) f(a + h) (C) f(a + h) - f(a) f(a + h) – f(a) (D) h # 0 h
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If g is the inverse of a function f, then f is the inverse of g.
Let f(x) = 3 - 2x. Find (A) f(2) (B) f(2 + h) (C) f(2 + h) – f(2) f(2 + h) - f(2) (D) ,h 0 h
Find the value of an investment of $10,000 in 12 years if it earns an annual rate of 3.95% compounded continuously.
For each rational function in Problem(A) Find any intercepts for the graph.(B) Find any vertical and horizontal asymptotes for the graph.(C) Sketch any asymptotes as dashed lines. Then sketch a graph
Given that f is a quadratic function with minimum f(x) = f(2) = 4, find the axis, vertex, range, and x intercepts.
For each rational function in Problem(A) Find any intercepts for the graph.(B) Find any vertical and horizontal asymptotes for the graph.(C) Sketch any asymptotes as dashed lines. Then sketch a graph
If f(x) = 5x + 1, find and simplify each of the following in Problem.f(4 - x)
If f(x) = 5x + 1, find and simplify each of the following in Problem.f(2x - 1)
If f(x) = 5x + 1, find and simplify each of the following in Problem.f(f( -1))
If f(x) = 5x + 1, find and simplify each of the following in Problem.f(f(0))
In Problem solve each equation for x. (Remember: ex ≠ 0 and e-x ≠ 0 for all values of x).e3x - 1 - e = 0
In Problem use point-by-point plotting to sketch the graph of each function. -66 f(x) 2 + x?
In Problem use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer.f(x) = 0 f(x) y = f(x) 10 5 -10 10 -5 - 10
In Problem use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer.f(x) = -5 f(x) y = f(x) 10 5 -10 10 -5 - 10
In Problem find the equations of any vertical asymptotes. x — х — 6 f(x) x² х? — Зх -10 ||
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The inverse of f(x) = 2x is g(x) = x/2.
In Problem use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer.f(x) = 0, x < 0 f(x) y =
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The inverse of f(x) = x2 is g(x) = √x.
In Problem use interval notation to write the solution set of the inequality.x2 + 7x + 12 ≥ 0
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If f is one-to-one, then the domain of f is equal to the range of f.
In Problem solve each equation for x. (Remember: ex ≠ 0 and e-x ≠ 0 for all values of x).e4x + e = 0
In Problem use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer.f(x) = 4 f(x) y = f(x) 10 5 -10 10 -5 - 10
In Problem use point-by-point plotting to sketch the graph of each function. 50 f(x) x² + 1
In Problem find the equations of any vertical asymptotes. x? + 3x f(x) %3D х3 — 36х
In Problem solve each equation for x. (Remember: ex ≠ 0 and e-x ≠ 0 for all values of x).e3x - 1 + e = 0
In Problem use interval notation to write the solution set of the inequality.x2 + x - 6 ≤ 0
In Problem solve each equation for x. (Remember: ex ≠ 0 and e-x ≠ 0 for all values of x).e4x - e = 0
In Problem solve each equation for x. (Remember: ex ≠ 0 and e-x ≠ 0 for all values of x).2x2ex - 8ex = 0
In Problem use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer.y = f(5) f(x) y = f(x) 10 5 -10 10 -5 - 10
In Problem solve each equation for x. (Remember: ex ≠ 0 and e-x ≠ 0 for all values of x).x2e-x - 9e-x = 0
In Problem use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer.y = f(-2) f(x) y = f(x) 10 5 -10 10 -5 - 10
In Problem use interval notation to write the solution set of the inequality.(x + 6) (x - 3) < 0
In Problem use interval notation to write the solution set of the inequality.(x - 3) (x + 5) > 0
In Problem find the equations of any vertical asymptotes. x² + 1 f(x) = (x² – 1)(x² – 9)
In Problem use the following graph of a function f to determine x or y to the nearest integer, as indicated. Some problems may have more than one answer.y = f(4) f(x) y = f(x) 10 5 -10 10 -5 - 10
Solve Problem for x to four decimal places.52x - 3 = 7.08

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