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college mathematics for business

Questions and Answers of College Mathematics For Business

In Problem convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form.4.35%
In Problem find the indicated quantity, givenPV = $8,000; PMT = ?; i = 0.0075; n = 60 1- (1 + i) PV = PMT – i
In Problem convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form.0.25%
Solve the equation 2,500 = 1,000(1.06)n for n to the nearest integer using:(A) Logarithms(B) Graphical approximation techniques or an equation solver on a graphing calculator
In Problem use the continuous compound interest formula (3) to find each of the indicated values.P = $2,450; r = 8.12%; t = 3 years; A = ?
In Problem find i (the rate per period) and n (the number of periods) for each loan at the given annual rate.Annual payments of $5,195 are made for 9 years to repay a loan at 5.48% compounded
In Problem convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form.0.0019
Solve the equationfor n to the nearest integer using:(A) Logarithms(B) Graphical approximation techniques or an equation solver on a graphing calculator. (1.01)" – 1 5,000 = 100- 0.01
In Problem convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form.0.0084
If you borrow $3,000 at 14% simple interest for 10 months, how much will you owe in 10 months? How much interest will you pay?
In Problem use the continuous compound interest formula (3) to find each of the indicated values.A = $6,300; r = 9.45%; t = 8 years; P = ?
In Problem convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form.0.36%
Grandparents deposited $6,000 into a grandchild’s account toward a college education. How much money (to the nearest dollar) will be in the account 17 years from now if the account earns 7%
In Problem convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a
How much should you pay for a corporate bond paying 6.6% compounded monthly in order to have $25,000 in 10 years?
In Problem use the continuous compound interest formula (3) to find each of the indicated values.A = $88,000; P = $71,153; r = 8.5%; t = ?
In Problem convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a
An investment account pays 5.4% compounded annually. Construct a balance sheet showing the interest earned during each year and the balance at the end of each year for 4 years if(A) A single deposit
In Problem convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a
In Problem use the continuous compound interest formula (3) to find each of the indicated values.A = $15,875; P = $12,100; t = 48 months; r = ?
In Problem convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a
A $10,000 retirement account is left to earn interest at 7% compounded daily. How much money will be in the account 40 years from now when the owner reaches 65?
In Problem convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a
A couple wishes to have $40,000 in 6 years for the down payment on a house. At what rate of interest compounded continuously must $25,000 be invested now to accomplish this goal?
In Problem use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.6.6% compounded quarterly
In Problem use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.3.84% compounded monthly
In Problem convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a
What is the value of an ordinary annuity at the end of 8 years if $200 per month is deposited into an account earning 7.2% compounded monthly? How much of this value is interest?
In Problem use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.5.52% compounded monthly
Explain what is meant by an ordinary annuity.
Explain how an ordinary annuity is involved when you take out an auto loan from a bank.
Explain what is meant by the present value of an ordinary annuity.
In Problem convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a
A payday lender charges $60 for a loan of $500 for 15 days. Find the annual interest rate. (Use a 360-day year.)
In Problem use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.2.94% compounded semiannually
The annual interest rate on a credit card is 25.74% and interest is calculated by the average daily balance method. The unpaid balance at the start of a 30-day billing cycle was $1,672.18. A purchase
In Problem use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.7.3% compounded daily
What will a $23,000 car cost (to the nearest dollar) 5 years from now if the inflation rate over that period averages 5% compounded annually?
In Problem use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.5.44% compounded quarterly
Problem refer to the area A and perimeter P of a rectangle with length l and width w (see the figure).The perimeter of a rectangle is 100 m. Express the area A(l) as a function of the length l, and
Problem refer to the area A and perimeter P of a rectangle with length l and width w (see the figure).The area of a rectangle is 81 sq in. Express the perimeter P(l) as a function of the length l,
Noting that p = 3.141 592 654 ... and √2=1.414 213 562 ... explain why the calculator results shown here are obvious. Discuss similar connections between the natural logarithmic function and the
For Problem solve each equation to four decimal places.ex = 0.3059
From the dawn of humanity to 1830, world population grew to one billion people. In 100 more years (by 1930) it grew to two billion, and 3 billion more were added in only 60 years (by 1990). In 2016,
A good approximation of the normal weight of a person 60 inches or taller but not taller than 80 inches is given by w(x) = 5.5x - 220, where x is height in inches and w(x) is weight in pounds.(A)
Graph Problem using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals.y = 2 ln(x + 2)
In Problem find and simplify each of the following, assuming h ≠ 0 in (C).f(x) = 4x2 - 7x + 6 (A) f(x + h) (B) f(x + h) - f(x) f(x + h) - f(x) (C) h
Under ideal conditions, if a person driving a vehicle slams on the brakes and skids to a stop, the speed of the vehicle v(x) (in miles per hour) is given approximately by v(x) = C√x, where x is the
Solve Problem exactly without using a calculator.ln(2x - 2) - ln(x - 1) = ln x
Solve Problem exactly without using a calculator.ln(x + 3) - ln x = 2 ln 2
Graph Problem using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals.y = 4 ln x - 3
Solve Problem exactly without using a calculator.log 3 x2 = 2 + log 9x
Write ln y = -5t + ln c in an exponential form free of logarithms. Then solve for y in terms of the remaining variables.
Explain why the logarithm of 1 for any permissible base is 0.
Explain why 1 cannot be used as a logarithmic base.
The following graph is the result of applying a sequence of transformations to the graph of y = 3√x. Describe the transformations verbally, and write an equation for the graph. y 7
Explain why 1 is not a suitable logarithmic base.
Problem refer to the area A and perimeter P of a rectangle with length l and width w (see the figure).The area of a rectangle is 25 sq in. Express the perimeter P(w) as a function of the width w, and
A company manufactures memory chips for microcomputers. Its marketing research department, using statistical techniques, collected the data shown in Table 8, where p is the wholesale price per chip
The table shows the electricity rates charged by Easton Utilities in the summer months.(A) Write a piecewise definition of the monthly charge S(x) (in dollars) for a customer who uses x kWh in a
Problem refer to the area A and perimeter P of a rectangle with length l and width w (see the figure).The perimeter of a rectangle is 160 m. Express the area A(w) as a function of the width w, and
Provident Bank of Cincinnati, Ohio, offered a certificate of deposit that paid 1.25% compounded quarterly. If a $5,000 CD earns this rate for 5 years, how much will it be worth?
Capital One Bank of Glen Allen, Virginia, offered a certificate of deposit that paid 1.05% compounded daily. If a $5,000 CD earns this rate for 5 years, how much will it be worth?
(A) Using the price–demand functionp(x) = 75 - 3x 1 ≤ x ≤ 20from Problem 85, write the company’s revenue function and indicate its domain.(B) Complete Table 10, computing revenues to
How long will it take for money invested at 6.59% compounded monthly to triple?
Use the cost and revenue functions from Problem 88.(A) Write a profit function and graph it in a graphing calculator.(B) Determine graphically when P = 0, P < 0, and P > 0 to the nearest
The research department in a company that manufactures AM/FM clock radios established the following price-demand, cost, and revenue functions:where x is in thousands of units, and C(x) and R(x) are
How many years (to two decimal places) will it take an investment of $35,000 to grow to $50,000 if it is invested at 4.75% compounded continuously?
A cordless screwdriver is sold through a national chain of discount stores. A marketing company established price–demand and price–supply tables (Tables 2 and 3), where x is the number of
How long will it take for money invested at 7.39% compounded continuously to double?
A construction company has 840 feet of chain-link fence that is used to enclose storage areas for equipment and materials at construction sites. The supervisor wants to set up two identical
A company is planning to introduce a 10-piece set of nonstick cookware. A marketing company established price–demand and price–supply tables for selected prices (Tables 1 and 2), where x is the
One leukemic cell injected into a healthy mouse will divide into 2 cells in about 12 day. At the end of the day these 2 cells will divide into 4. This doubling continues until 1 billion cells are
According to data published by the FBI, the crime index in the United States has shown a downward trend since the early 1990s (Table 3).(A) Find a cubic regression model for the crime index if x = 0
The annual expenditures for Medicare (in billions of dollars) by the U.S. government for selected years since 1980 are shown in Table 5. Let x represent years since 1980.(A) Find an exponential
The intensity of light entering water is reduced according to the exponential equationI = I 0e-kdwhere I is the intensity d feet below the surface, I0 is the intensity at the surface, and k is the
The number of dairy cows on farms in the United States is shown in Table 4 for selected years since 1950. Let 1940 be year 0.(A) Find a logarithmic regression model (y = a + b ln x) for the data.
The population of some countries has a relative growth rate of 3% (or more) per year. At this rate, how many years (to the nearest tenth of a year) will it take a population to double?
In Problem find the indicated quantity, given A = P(1 + rt).A = ?; P = $100; r = 9%; t = 6 months
In Problem find the indicated quantity, given A = P(1 + rt).A = $808; P = ?; r = 12%; t = 1 month
In Problem find the indicated quantity, given A = P(1 + rt).A = $4,120; P = $4,000; r = ?; t = 6 months
In Problem find the indicated quantity, given A = P(1 + rt).A = $212; P = $200; r = 8%; t = ?
In Problem find the indicated quantity, given A = P(1 + i)n.A = ?; P = $1,200; i = 0.005; n = 30
In Problem find the indicated quantity, given A = P(1 + i)n.A = $5,000; P = ?; i = 0.0075; n = 60
In Problem find the indicated quantity, given A = Pert.A = ?; P = $4,750; r = 6.8%; t = 3 years
In Problem find the indicated quantity, given A = Pert.A = $36,000; P = ?; r = 9.3%; t = 60 months
In Problem find i (the rate per period) and n (the number of periods) for each loan at the given annual rate.Monthly payments of $245.65 are made for 4 years to repay a loan at 7.2% compounded
In Problem find the indicated quantity, givenFV = ?; PMT = $1,000; i = 0.005; n = 60 (1 + i)" – 1 PMT FV = i
In Problem convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form.6.2%
In Problem use point-by-point plotting to sketch the graph of each function. 8 f(x)
Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. f(x) -5 5
Table 3 shows the per capita consumption of ice cream in the United States for selected years since 1987.(A) Let x represent the number of years since 1980 and find a cubic regression polynomial for
For Problem find x, y, or b without using a calculator.logb 10,000 = 2
In Problem assume that a, b, c, h, and k are constants with a ≠ 0 such thatax2 + bx + c = a(x - h)2 + kfor all real numbers x.Show that b h = 2a
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.6x -
A person wishes to have $15,000 cash for a new car 5 years from now. How much should be placed in an account now, if the account pays 6.75% compounded weekly? Compute the answer to the nearest dollar.
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(x
Refer to Table 4.(A) Let x represent the number of years since 2000 and find a cubic regression polynomial for the per capita consumption of eggs.(B) Use the polynomial model from part (A) to
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-3
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

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