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Questions and Answers of Mathematics Economics Business

(A) Sketch a graph of f(x) = –x2 + 5x + 3 in a rectangular coordinate system.(B) Find x and y intercepts algebraically to four decimal places.(C) Graph f(x) = –x2 + 5x + 3 in a standard viewing
A company that manufactures computers has established that, on the average, a new employee can assemble N(t) components per day after t days of on-the-job training, as given bySketch a graph of N, 0
Table 2 gives the market value of a hybrid sedan (in dollars) x years after its purchase. Find an exponential regression model of the form y = abx for this data set. Estimate the purchase price of
Use the revenue function from Example 3 and the cost function from Matched Problem 3:Both have domain 1 ≤ x ≤ 15.(A) Sketch the graphs of both functions in the same coordinate system.(B)
Write in simpler form, as in Example 4.Data from Example 4Use logarithmic properties to write in simpler form:logb wx/yzlogb (wx)3/5 ex loge bloge x/loge b (A) logb R ST (B) logb R 2/3 S (C) 2u
Table 3 gives the market value of a midsize sedan (in dollars) x years after its purchase. Find an exponential regression model of the form y = abx for this data set. Estimate the purchase price of
The graph of y = G(x) in Figure 9 involves a reflection and a translation of the graph of y = x3. Describe how the graph of function G is related to the graph of y = x3 and find an equation of the
(A) How are the graphs of y = 2|x| and y = 0.5|x|related to the graph of y = |x|? Confirm your answer by graphing all three functions simultaneously in the same coordinate system.(B) How is the graph
Find the domains of functions f, g, and h: f(x) = 12 X - g(x) = 1 - x² h(x) = √x - 1 Vx
Refer to Table 1. Use quadratic regression to find the best model of the form y = ax2 + bx + c for boat speed y (in miles per hour) as a function of engine speed x (in revolutions per minute).
Find x so that3/2 logb 4 – 2/3 logb 8 + logb 2 = logb x
If $1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10 years? Compute the answer to the nearest cent.
Find the domains of functions F, G, and H: F(x)=x²-3x + 1 G(x) 54 x + 3 H(x) = V2 - x
Find x so that 3 logb 2 + 1/2 logb 25 – logb 20 = logb x.
If you deposit $5,000 in an account paying 9% compounded daily, how much will you have in the account in 5 years? Compute the answer to the nearest cent.
Table 1 gives performance data for a boat powered by an Evinrude outboard motor. Use quadratic regression to find the best model of the form y = ax2 + bx + c for fuel consumption y (in miles per
Discuss the relationship between the graphs of y = - |x - 3| + 1 and y = |x|. Confirm your answer by graphing both functions simultaneously in the same coordinate system.
Graph the piecewise-defined function -2x + 4 x 1 if 0 ≤ x ≤ 2 if x > 2
For f(x) = x2 – 2x + 7, find (A) f(a) (C) f(a+h)-f(a) (B) f(a+h) (D) f(a+h)-f(a), n = 0 h
Solve: log10 x + log10 (x + 1) = log106.
If $1,000 is invested in an account paying 10% compounded continuously, how much will be in the account at the end of 10 years? Compute the answer to the nearest cent.
Repeat Example 6 for f(x) = x2 – 4x + 9.Data from Example 6For f(x) = x2 – 2x + 7, find (A) f(a) (C) f(a+h)-f(a) (B) f(a+h) (D) f(a+h)-f(a), n = 0 h
Solve: log3 x + log3(x – 3) = log3 10.
Graph the piecewise-defined function g(x) [x+1_if 0 ≤ x < 2 105x if x ≥ 2
If you deposit $5,000 in an account paying 9% compounded continuously, how much will you have in the account in 5 years? Compute the answer to the nearest cent.
Trussville Utilities uses the rates shown in Table 2 to compute the monthly cost of natural gas for residential customers. Write a piecewise definition for the cost of consuming x CCF of natural gas
The financial department in Example 7, using statistical techniques, produced the data in Table 6, where C(x) is the cost in millions of dollars for manufacturing and selling x million cameras.Using
A manufacturer of a popular digital camera wholesales the camera to retail outlets throughout the United States. Using statistical methods, the financial department in the company produced the
Use a calculator to evaluate each to six decimal places:(A) log 3,184 (B) ln 0.000 349 (C) log (–3.24)
Use a calculator to evaluate each to six decimal places:(A) log 0.013 529 (B) ln 28.693 28 (C) ln (–0.438)
Easton Utilities uses the rates shown in Table 1 to compute the monthly cost of natural gas for each customer. Write a piecewise definition for the cost of consuming x CCF (cubic hundred feet) of
Find x to four decimal places, given the indicated logarithm:(A) log x = –2.315 (B) ln x = 2.386
Solve for x to four decimal places:(A) 10x = 2 (B) ex = 3 (C) 3x = 4
Solve for x to four decimal places:(A) 10x = 7 (B) ex = 6 (C) 4x = 5
How long (to the next whole year) will it take money to double if it is invested at 20% compounded annually?
How long (to the next whole year) will it take money to triple if it is invested at 13% compounded annually?
Refer to Example 11. Use the model to predict the home ownership rate in the United States in 2030 (to the nearest tenth of a percent).Data from Example 11The U.S. Census Bureau published the data in
The U.S. Census Bureau published the data in Table 1 on home ownership rates. Let x represent time in years with x = 0 representing 1900. Use logarithmic regression to find the best model of the form
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = –2x; f(x) = 2x
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = 2x – 2; f(x) = 2x
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = 3x + 1; f(x) = 3x
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = –3x; f(x) = 3x
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = ex + 1; f(x) = ex
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = ex – 2; f(x) = ex
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = 2e–(x + 2); f(x) = e–x
In Problem describe verbally the transformations that C can be used to obtain the graph of g from the graph of f.g(x) = 0.5e–(x – 1); f(x) = e–x
In Problem evaluate the expression without using a calculator.ln e–3
In Problem evaluate the expression without using a calculator.eln(–1)
In Problem evaluate the expression without using a calculator.eln(–3)
In Problem evaluate the expression without using a calculator.ln e–1
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexampleThe graph of a one-to-one function intersects each vertical line exactly
In Problem the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using –5 ≤ x ≤ 5
In Problem the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using –5 ≤ x ≤ 5
Solve Problem graphically to two decimal places using a graphing calculator.2 – 5x – x2 = 0
In Problem the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using –5 ≤ x ≤ 5
Solve Problem graphically to two decimal places using a graphing calculator.1.9x2 – 1.5x – 5.6 < 0
In Problem the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using –5 ≤ x ≤ 5
Let f(x) = x2 – 3x + 1. Find(A) f(a) (B) f(a + h)(C) f(a + h) - f(a)(D) f(a+h)-f(a) h -, h = 0
Solve Problem graphically to two decimal places using a graphing calculator.2.8 + 3.1x – 0.9x2 ≤ 0
Graph Problem by converting to exponential form first.y = log2 (x – 2)
Explain how the graph of the equation in Problem 55 can be obtained from the graph of y = log2 x using a simple transformationData from Problem 55Graph Problem by converting to exponential form
Changing the order in a sequence of transformations may change the final result. Investigate each pair of transformations in Problem to determine if reversing their order can produce a different
For Problem, evaluate to five decimal places using a calculator.(A) log 3,527.2(B) log 0.006 913 2(C) ln 277.63(D) ln 0.040 883
In Problem find and simplify the expression if f(x) = x2 – 4.f(5x)
In Problem find and simplify the expression if f(x) = x2 – 4.f(–3x)
For Problem find x to four decimal places.(A) log x = 1.1285(B) log x = –2.0497(C) ln x = 2.7763(D) ln x = –1.8879
Changing the order in a sequence of transformations may change the final result. Investigate each pair of transformations in Problem to determine if reversing their order can produce a different
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The graph of every rational function has at least one vertical asymptote.
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The graph of every exponential function has a horizontal asymptote.
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The graph of every logarithmic function has a vertical asymptote.
In Problem find and simplify the expression if f(x) = x2 – 4.f(2) + f(h)
Let p(x) = ln x, q(x) = √x, and r(x) = x. Use a graphing calculator to draw graphs of all three functions in the same viewing window for 1 ≤ x ≤ 16. Discuss what it means for one function to be
The area of a rectangle is 25 sq in. Express the perimeter P(w) as a function of the width w, and state the domain of this function.
The perimeter of a rectangle is 100 m. Express the area A(l) as a function of the length l, and state the domain of this function.
In a study of the speed of muscle contraction in frogs under various loads, British biophysicist A. W. Hill determined that the weight w (in grams) placed on the muscle and the speed of contraction v
Table 4 shows the yield (in bushels per acre) and the total production (in millions of bushels) for corn in the United States for selected years since 1950. Let x represent years since 1900. Find a
Refer to Table 4. Find a logarithmic regression model (y = a + b ln x) for the total production. Estimate (to the nearest million) the production in 2024. Table 4 United States Corn Production Yield
If the world population is now 7.4 billion people and if it continues to grow at an annual rate of 1.1% compounded continuously, how long (to the nearest year) would it take before there is only 1
In Problem find the sum of the finite geometric series a + ar + ar2 + g+ arn – 1.1 + 2 + 4 + 8 + · · · + 29
(A) Your sister has loaned you $1,000 with the understanding that you will repay the principal plus 4% simple interest when you can. How much would you owe her if you repaid the loan after 1 year?
If $1,000 is invested at 8% compounded(A) Annually,(B) Semiannually,(C) Quarterly,(D) Monthly, What is the amount after 5 years? Write answers to the nearest cent.
Repeat Example 1 with an annual interest rate of 6% over an 8-year period.Data from Example 1If $1,000 is invested at 8% compounded(A) Annually,(B) Semiannually,(C) Quarterly,(D) Monthly, What is
Find the total amount due on a loan of $800 at 9% simple interest at the end of 4 months.
In Problem solve the equation for the unknown quantity.1,641.6 = P(1.2)3
To purchase a home, a family plans to sign a mortgage of $70,000 at 8% on the unpaid balance. Discuss the advantages and disadvantages of a 20-year mortgage as opposed to a 30-year mortgage. Include
Find the total amount due on a loan of $500 at 12% simple interest at the end of 30 months.
(A) Discuss the similarities and differences in the graphs of future value FV as a function of time t for ordinary annuities in which $100 is deposited each month for 8 years and interest is
What is the value of an annuity at the end of 20 years if $2,000 is deposited each year into an account earning 8.5% compounded annually? How much of this value is interest?
How much should you deposit in an account paying 8% compounded quarterly in order to receive quarterly payments of $1,000 for the next 4 years?
If your state sales tax rate is 5.65%, how much tax will you pay on a bicycle that sells for $449.99?
Graph 3x – 4y = 12 on a graphing calculator and find the intercepts.
In Problem find the sum of the finite geometric series a + ar + ar2 + · · · + arn – 1. Write the answer as a quotient of integers. - + -10 + - + - + 1 +
In Problem solve the equation for the unknown quantity.2,488.32 = 1,000(1.2)n
Return to Example 2 and solve each system by substitution. Based on your results, describe how you can recognize a dependent system or an inconsistent system when using substitution.Data from Example
Solve using augmented matrix methods: 2x₁ - 3x₂ = 6 1 2 3x1 + 4x2 ||
Solve using augmented matrix methods:5x1 – 2x2 = 112x1 + 3x2 = 5/2
In Problem find the x and y coordinates of the intersection of the given lines.y = 5x + 7 and the x axis
Solve using augmented matrix methods: 2x₁ - x₂ = x2 -6x₁ + 3x₂ 4 -12 (8)
Solve to two decimal places using graphical approximation techniques on a graphing calculator:5x + 2y = 152x – 3y = 16
Solve using augmented matrix methods:–2x1 + 6x2 = 63x1 – 9x2 = –9

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