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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
Use the revenue function from Problem 62, in this exercise and the given cost function: R(x) = x:(2,000 - 60x) Revenue function C(A-) = 4,000 + 500x Cost function where x is thousands of computers, and C(x) and R(x)are in thousands of dollars. Both functions have domain 1 ≤ .v ≤ 25. (A)
Use the revenue and cost functions from Problem 64 in this exercise: R(x) = x-(2,000 - 60x) Revenue function C(x) = 4,000 + 500x: Cost function where x is thousands of computers, and R(x)and C(A:) are in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25. (A) Form a profit function P,
Find the distance from the center that the rate of flow is 30 centimeters per second. Round answer to two decimal places.Problem67The 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 table gives performance data for a boat powered by an Evinrude outboard motor. Find a quadratic regression model (y = ax2 + bx + c)for fuel consumption y (in miles per gallon) as a function of engine speed (in revolutions per minute). Estimate the fuel consumption at an engine speed of 2,300
In Problem, for each polynomial function find the following: (A) Degree of the polynomial (B) Allx intercepts (C) The y intercept f (x) = (x8 + 5)(x12 + 7)
In Problem, for each polynomial function find the following: (A) Degree of the polynomial (B) Allx intercepts (C) The y intercept f (x) = 4 - 3x
For each rational function in Problem,(A) Find the intercepts for the graph.(B) Determine the domain.(C) Find any vertical or horizontal asymptotes for the graph.(D) Sketch any asymptotes as dashed lines. Then sketch a graph of y = f(x) for-10 ‰¤ x ‰¤ 10 and-10
For each rational function in Problem,(A) Find the intercepts for the graph.(B) Determine the domain.(C) Find any vertical or horizontal asymptotes for the graph.(D) Sketch any asymptotes as dashed lines. Then sketch a graph of y = f(x) for-10 ‰¤ x ‰¤ 10 and-10
For each rational function in Problem,(A) Find the intercepts for the graph.(B) Determine the domain.(C) Find any vertical or horizontal asymptotes for the graph.(D) Sketch any asymptotes as dashed lines. Then sketch a graph of y = f(x) for-10 ‰¤ x ‰¤ 10 and-10
Compare the graph of y = x3 to the graph of y = x3 - 2x + 2 in the following two viewing windows:(A) -5 ≤ x ≤ 5, -5 ≤ y ≤ 5(B) -5 ≤ x ≤ 5, -500 ≤ y ≤ 500
Compare the graph of y = -x5 to the graph of y = -x5 + 5x3 - 5x + 2 in the following two viewing windows:(A) -5 ≤ x ≤ 5, -5 ≤ y ≤ 5(B) -5 ≤ x ≤ 5. -500 ≤ y ≤ 500
In Problem, for each polynomial function find the following: (A) Degree of the polynomial (B) Allx intercepts (C) The y intercept f (x) = 5x - x2 - 6
In problem find the equation of any vertical asymptotes
In Problem find the equations of any vertical asymptotes
In Problem find the equations of any vertical asymptotes.
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 off f for -10 ‰¤ x ‰¤ 10 and -10 ‰¤ y ‰¤ 10.(D) Graph the function in a standard
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 off f for -10 ‰¤ x ‰¤ 10 and -10 ‰¤ y ‰¤ 10.(D) Graph the function in a standard
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 off f for -10 ‰¤ x ‰¤ 10 and -10 ‰¤ y ‰¤ 10.(D) Graph the function in a standard
A company manufacturing surfboards has fixed costs of $300 per day and total costs of $5,100 per day at a daily output of 20 boards. (A)Assuming that the total cost per day, C(x),is linearly related to the total output per day, x, write an equation for the cost function. (B) The average cost per
In Problem, for each polynomial function find the following: (A) Degree of the polynomial (B) Allx intercepts (C) The y intercept f (x) = (x + 7 )(x - 4)
Financial analysts in a company that manufactures DVD players arrived at the following daily cost equation for manufacturing x DVD players per day: C(.v) = x2 + 2x + 2,000 The average cost per unit at a production level of x players per day is (x)=C(x)/x. (A) Find the rational function . (B)
The financial department of a hospital, using statistical methods, arrived at the cost equation C(x)= 20x3 - 360x2 + 2,300x - 1,000 1 ≤ x ≤ 12 where C(x)is the cost in thousands of dollars for handling .v thousand cases per month. The average cost per case is given by (x) = C{x)lx. (A) Write
(A) Let x represent the number of years since 1980 and find a cubic regression polynomial for the per capita consumption of eggs.(B) Use the polynomial model from part (A) to estimate (to the nearest integer) the per capita consumption of eggs in 2020.
In 1917, L. L. Thurstone, a pioneer in quantitative learning theory, proposed the rational functionto model the number of successful acts per unit time that a person could accomplish after x practice sessions. Suppose that for a particular person enrolled in a typing class, where f(x) is the number
(A) Let x represent the number of years since 1950 and find a cubic regression polynomial for the divorce rate. (B) Use the polynomial model from part (A) to estimate the divorce rate (to one decimal place) for 2020.
In Problem, for each polynomial function find the following: (A) Degree of the polynomial (B) Allx intercepts (C) The y intercept f (x) = (2 - 5x)(x -6)(x + 1)
Graph each function in Problem over the indicated interval. y = -ex; [-3, 3]
Match each equation with the graph of f, g, h, or k in the figure.(A) y=(1/4)x(B) y=(0.5)x(C) y=5X(D) y=3X
Use the graph of/shown in the figure to sketch the graph of each of the following.(A) y=f(x)+2(B) y=f(x- 3)(C) y=2f(x)- 4(D) y=4 - f(x+2)
In Problem, graph each function over the indicated interval. G(t)=3t/100; [-200,200]
In Problem, graph each function over the indicated interval. y = 2 + ex-2; [-1,5]
In Problem, graph each function over the indicated interval.
Find real numbers a and b such that a ≠ b but a4 = b4. Explain why this does not violate the third exponential function property in Theorem 2 on page 98.
Solve equation in Problem for x. 53x = 54x -2
Solve equation in problem for x. 7x2 = 72x +3
Solve equation in problem for x (1 - x)5 = (2x - 1)5
Solve Equation in Problem for x. (Remember: ex ≠ 0 and e-x ≠ 0.) 2xe-x = 0
Solve Equation in Problem for x. (Remember: ex ≠ 0 and e-x ≠ 0.) x2ex - 5xex = 0
Graph each function in Problem over the indicated interval. y = 3x;[-3,3]
Graph each function in Problem over the indicated interval. m(x)=x(3-x); [0, 3]
Graph each function in problem over the indicated interval.
Find the value of an investment of $24,000 in 7 years if it earns an annual rate of 4.35% compounded continuously. In Problem involving days, a 365-day year is assumed
Suppose that $4,000 is invested at 6% compounded weekly. How much money will be in the account in (A) 1/2year? (B) 10 years? Compute answers to the nearest cent. In Problem involving days, a 365-day year is assumed
A couple just had a baby. How much should they invest now at 5.5% compounded daily in order to have $40,000 for the child's education 17 years from now? Compute the answer to the nearest dollar. In Problem involving days, a 365-day year is assumed
Refer to Problem 49. The following rates for 60-month certificates of deposit were also taken from BanxQuote Web sites: (A) Oriental Bank & Trust, 5.50% compounded quarterly (B) BMW Bank of North America, 5.12% compounded monthly (C) Bank First Corporation, 4.86% compounded daily Compute the value
People assigned to assemble circuit boards for a computer manufacturing company undergo on-the-job training. From past experience, the learning curve for the average employee is given by N = 40(1 - e-0.l2t) where N is the number of boards assembled per day after / days of training. Graph this
(A) Let x represent the number of years since 1990 and find an exponential regression model (y = abx) for the average salary in the NBA. Use the model to estimate the average salary (to the nearest thousand dollars) in 2020. (B) The average salary in the NBA in 1997 was $2.2 million. How does this
Refer to Problem 55. Light intensity I relative to depth d (in feet) for one of the clearest bodies of water in the world, the Sargasso Sea, can be approximated bywhere I0 is the intensity of light at the surface. What percentage of the surface light will reach a depth of (A) 50 feet? (B) 100 feet?
In 2008, the estimated population in Ethiopia was 83 million people with a relative growth rate of 3.2%. (A) Write an equation that models the population growth in Ethiopia, letting 2008 be year 0. (B) Based on the model, what is the expected population in Ethiopia (to the nearest million) in 2020?
Graph each function in Problem over the indicated interval. y = (1/3)x = -3-x; [-3,3]
Table 6 shows the life expectancy (in years) at birth for residents of the United States from 1970 to 2005. Let x represent years since 1970. Find an exponential regression model for this data and use it to estimate the life expectancy for a person born in 2015.
Graph each function in Problem over the indicated interval. g(x) = -3-x; [-3, 3]
For Problem, evaluate without a calculator. loge 1
For Problem, evaluate without a calculator. log10 10
For Problem, evaluate without a calculator. Log3 35
For Problem, evaluate without a calculator. Log6 36
For problem find x, y, or b without a calculator. log2 x = 2
For problem fin x, y, or b without a calculator. log3 27 = y
For problem find x, y, or b without a calculator. logb e-2 = -2
For problem find x, y, or b without a calculator. Log25 x = 1/2
Find x in Problem Logb x = 2/3logb 27 + 2 logb 2 - logb 3
Find x in Problem logb x = 3 logb 2 + 1/2logb 25 - logb 20
Find x in Problem logb(x + 2) + logb x = logb 24
Find x in Problem log10(x + 6) - log10(x- 3) = 1
Graph problem by converting to exponential form first y = log3 (x +2 )
What are the domain and range of the function defined by y = log (x - 1) -1?
For Problem, evaluate to five decimal places using a calculator. (A) log 72.604 (B) log 0.033041 (C) ln 40,257 (D) ln 0.005 926 3
For Problem, find x to four decimal places. (A) log x = 2.0832 (B) log x = -1.1577 (C) ln x = 3.1336 (D) In x= -4.3281
For problem, solve equation to four decimal places. 10x = 153
For problem, solve equation to four decimal places. ex = 0.3059
For problem, solve equation to four decimal places. 1.024t = 2
Graph Problem using a calculator and point-by-pint plotting. Indicate increasing and decreasing intervals. y = - In x
Graph Problem using a calculator and point-by-pint plotting. Indicate increasing and decreasing intervals. y = In |x|
Graph Problem using a calculator and point-by-pint plotting. Indicate increasing and decreasing intervals. y = 2 In x + 2
Graph Problem using a calculator and point-by-pint plotting. Indicate increasing and decreasing intervals. y = 4 In(x - 3)
Let p(x)=logx, q(x) = 3√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 smaller than another on an interval, and then order the three functions from smallest to largest for
In its first 10 years the Janus Flexible Income Fund produced an average annual return of 9.58%. Assume that money invested in this fund continues to earn 9.58% compounded annually. How long will it take money invested in this fund to double?
How many years (to two decimal places) will it take $5,000 to grow to $7,500 if it is invested at 8% com-pounded semiannually? Compounded monthly?
Archaeology: carbon-14 dating. The radioactive carbon-14 (14C) in an organism at the time of its death decays according to the equation A = A0e-0.000124t where t is time in years and A0 is the amount of 14C present at time i = 0.Estimate the age of a skull uncovered in an archaeological site if 10%
How many years (to two decimal places) will it take an investment of $ 17.000 to grow to $41,000 if it is invested at 2.95% compounded continuously?
Use the models constructed in Problem 85 to find the equilibrium point. Write the equilibrium price to the nearest cent and the equilibrium quantity to the nearest unit.
Sound intensity: decibels. Use the formula in Problem 87 (with I0 = 10-l6W/cm2) to find the decibel ratings of the following sounds: (A) Whisper: 10-13 W/cm2 (B) Normal conversation: 3.16 × 10-10 W/cm2 (C) Heavy traffic: 10-8 W/cm2 (D) Jet plane with afterburner: 10-1 W/cm2
Refer to Table 3. Find a logarithmic regression model (y = a+b In x)for the total production. Estimate (to the nearest million) the production in 2020.
In problem, use formula (1) for simple interest to find each of the indicated quantities. I = $950; r = 9% ; t = 1 year ; I = ?
In problem, use formula (1) for simple interest to find each of the indicated quantities. I = $15; P = $600 ; t = 240 days ; r = ?
In problem, use formula (1) for simple interest to find each of the indicated quantities. I = $28; P = $700; t = 13 weeks ; r = ?
In problem, use formula (1) for simple interest to find each of the indicated quantities. I = $96; P = $3,200 ; r = 4% ; t = ?
In Problem, use formula (2) for the amount to find each of the indicated quantities. A = $3,000; P = 4.5%; r = 30days; A = ?
In Problem, use formula (2) for the amount to find each of the indicated quantities. A = $6,608; P = 24% ; t = 3quarters; P = ?
In Problem, use formula (2) for the amount to find each of the indicated quantities. A = $22,135; P = $19,000; r = 39weeks; r = ?
In Problem, use formula (2) for the amount to find each of the indicated quantities. A = $410; P = $400; r = 10%; t = ?
In Problem, solve each formula for the indicated variable. I = Prt ; for P
In Problem, solve each formula for the indicated variable. A = P + Prt ; for r
If $5,000 is loaned for 9 months at a 6.2% annual rate, how much interest is earned?
A department store charges an 18% annual rate for overdue accounts. How much interest will be owed on an $835 account that is 2 months overdue?
A loan of $10,000 was repaid at the end of 6 months. What amount (principal and interest) was repaid, if a 6.5% annual rate of interest was charged?
A check for $3,097.50 was used to retire a 5-month $3,000 loan. What annual rate of interest was charged?
If you paid $120 to a loan company for the use of $2,000 for 90 days, what annual rate of interest did they charge?
George finds a company that charges 59$ per day for each $1,000 borrowed. If he borrows $3,000 for 60 days, what amount will he repay, and what annual interest rate will he pay the company?
What annual interest rate is earned by a 33-day T-bill with a maturity value of $1,000 that sells for $996.16?
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