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mathematics
college mathematics for business economics
Questions and Answers of
College Mathematics For Business Economics
How long will it take money to double if it is invested at 6% compounded monthly? 9% compounded monthly? (Round up to the next-higher month if not exact.)
In Problems 27–32, use the given interest rate i per compounding period to find r, the annual rate.2.1% per half year.
In Problems 27–32, use the given interest rate i per compounding period to find r, the annual rate.1.4% per quarter.
If $1,000 is deposited at the end of each year for 5 years into an ordinary annuity earning 8.32% compounded annually, construct a balance sheet showing the interest earned during each year and the
If $2,000 is deposited at the end of each quarter for 2 years into an ordinary annuity earning 7.9% compounded quarterly, construct a balance sheet showing the interest earned during each quarter and
A family needs $5,000 to finance an addition to their home. If the local credit union is willing to lend them the money at 0.8% per month on the unpaid balance, and asks for the money to be paid back
Beginning in January, a person plans to deposit $100 at the end of each month into an account earning 6% compounded monthly. Each year taxes must be paid on the interest earned during that year. Find
If $8,000 is invested at 7% compounded continuously, what is the amount after 6 years?
Bob makes his first $1,000 deposit into an IRA earning 6.4% compounded annually on his 24th birthday and his last $1,000 deposit on his 35th birthday (12 equal deposits in all). With no additional
You want to purchase an automobile for $27,300. The dealer offers you 0% financing for 60 months or a $5,000 rebate. You can obtain 6.3% financing for 60 months at the local bank. Which option should
If $1,000 is invested in an account that earns 9.75% compounded annually for 6 years, find the interest earned during each year and the amount in the account at the end of each year. Organize your
Compubank, an online banking service, offered a money market account with an APY of 1.551%.(A) If interest is compounded monthly, what is the equivalent annual nominal rate? (B) If you wish to have
If an investment company pays 6% compounded semiannually, how much should you deposit now to have $10,000 (A) 5 years from now? (B) 10 years from now?
American Express’s online banking division offered a money market account with an APY of 2.243%. (A) If interest is compounded monthly, what is the equivalent annual nominal rate? (B) If a
Construct the amortization schedule for a $1,000 debt that is to be amortized in four equal quarterly payments at 2.5% interest per quarter on the unpaid balance.
An ordinary annuity pays 7.44% compounded monthly. (A) A person deposits $100 monthly for 30 years and then makes equal monthly withdrawals for the next 15 years, reducing the balance to zero. What
How long will it take money to double if it is invested at (A) 10% compounded quarterly? (B) 12% compounded quarterly?
What annual nominal rate compounded monthly has the same annual percentage yield as 7.28% compounded quarterly?
How long will it take money to double if it is invested at (A) 9% compounded continuously? (B) 11% compounded continuously?
A person purchased a $145,000 home 10 years ago by paying 20% down and signing a 30-year mortgage at 7.9% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid
A newborn child receives a $20,000 gift toward college from her grandparents. How much will the $20,000 be worth in 17 years if it is invested at 7% compounded quarterly?
What will a $210,000 house cost 10 years from now if the inflation rate over that period averages 3% compounded annually?
In Problems 65–68, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. A
Rental costs for office space have been going up at 4.8% per year compounded annually for the past 5 years. If office space rent is now $25 per square foot per month, what were the rental rates 5
If the population in a particular country is growing at 1.7% compounded continuously, how long will it take the population to double? (Round up to the next-higher year if not exact.)
If the world population is now about 7.5 billion people and is growing at 1.1% compounded continuously, how long will it take the population to grow to 10 billion people? (Round up to the next-higher
(A) If an investment of $100 were made in 1776, and if it earned 3% compounded quarterly, how much would it be worth in 2026? (B) Discuss the effect of compounding interest monthly, daily, and
A promissory note will pay $50,000 at maturity 6 years from now. If you pay $28,000 for the note now, what rate compounded continuously would you earn?
How long will it take money to double if it is invested at 7% compounded daily? 8.2% compounded continuously?
How long does it take for a $4,800 investment at 8% compounded monthly to be worth more than a $5,000 investment at 5% compounded monthly?
One investment pays 10% simple interest and another pays 7% compounded annually. Which investment would you choose? Why?
What is the annual nominal rate compounded daily for a bond that has an annual percentage yield of 6.8%?
An online bank listed a money market account that earns 1.02% compounded daily. Find the APY as a percentage, rounded to three decimal places.
An online bank listed a 1-year CD that earns 1.25% compounded monthly. Find the APY as a percentage, rounded to three decimal places.
In Problems 1–10, for each polynomial function find the following:f(x) = 50 - 5x(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
Graph each function in Problems 3–10 over the indicated interval. y = 5; [-2, 2]
In Problems 1–10, for each polynomial function find the following:f(x) = 72 + 12x(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
Graph each function in Problems 3–10 over the indicated interval. y = (²)* = 5¹; [-2,2]
In Problems 1–10, for each polynomial function find the following:f(x) = x4(x - 1)(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
In Problems 1–10, for each polynomial function find the following:f(x) = x3(x + 5)(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
Graph each function in Problems 3–10 over the indicated interval. y = ()* = 3; [-3,3]
In Problems 1–10, for each polynomial function find the following:f(x) = x2 + 3x + 2(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
Graph each function in Problems 3–10 over the indicated interval. f(x) = -5%; [-2, 2]
In Problems 1–10, for each polynomial function find the following:f(x) = x2 - 4x - 5(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
Graph each function in Problems 3–10 over the indicated interval. g(x) = -3; [-3, 3]
In Problems 1–10, for each polynomial function find the following:f(x) = (x2 - 1)(x2 - 9)(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
Graph each function in Problems 3–10 over the indicated interval. y = -e-x; [-3, 3]
In Problems 1–10, for each polynomial function find the following:f(x) = (x2 - 4) (x3 + 27)(A) Degree of the polynomial (B) All x intercepts (C) The y intercept
In Problems 1–10, for each polynomial function find the following:(A) Degree of the polynomial (B) All x intercepts (C) The y intercept f(x) = (2x + 3)(x - 5)5
Graph each function in Problems 3–10 over the indicated interval. y = -e; [-3, 3]
In Problems 1–10, for each polynomial function find the following:(A) Degree of the polynomial (B) All x intercepts (C) The y intercept f(x) = (x + 3)²(8x - 4)6
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
In Problems 13–20, evaluate the expression without using a calculator.log10 100
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
In Problems 13–20, evaluate the expression without using a calculator.log10 100,000
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
In Problems 13–20, evaluate the expression without using a calculator.log2 16
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
In Problems 13–20, evaluate the expression without using a calculator.log3 1/3
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
In Problems 13–20, evaluate the expression without using a calculator.log5 1/25
Each graph in Problems 11–18 is the graph of a polynomial function. Answer the following questions for each graph:(A) What is the minimum degree of a polynomial function that could have the
In Problems 13–20, evaluate the expression without using a calculator.log41
In Problems 13–20, evaluate the expression without using a calculator. In 4 e
In Problems 13–20, evaluate the expression without using a calculator. In es
In Problems 21–26, graph each function over the indicated interval. f(t) = 2/10; [-30, 30]
In Problems 21–26, graph each function over the indicated interval. y = -3 + e¹+x; [-4,2]
For Problems 27–34, find x, y, or b without a calculator.log3 x = 2
Solve each equation in Problems 29–34 for x. 102 - 3x = 105x - 6
Solve each equation in Problems 29–34 for x. 53x = 54x - 2
Solve each equation in Problems 29–34 for x.45x - x2 = 4-6
Solve each equation in Problems 29–34 for x.7x2 = 72x+3
In Problems 41–46, find the equations of any vertical asymptotes. f(x) = = 2x + 5 (x² - 4)(x²-16)
Solve each equation in Problems 29–34 for x.53 = (x + 2)3
Solve each equation in Problems 29–34 for x.(1 - x)5 = (2x - 1)5
Find x in Problems 43–50. log, x = logb 8 + log, 9 - log, 6
Graph each function in Problems 43–46 over the indicated interval. h(x) = x(2); [-5,0]
Find x in Problems 43–50. log, x = log 27 + 2log 2 - log
In Problems 41–46, find the equations of any vertical asymptotes. f(x) x²8x + 7 X x² + 7x - 8
Find x in Problems 43–50. logbx = logb 4-log, 8 + 2log 2
In Problems 41–46, find the equations of any vertical asymptotes. f(x) = x² + 3x X - 36x
Find x in Problems 43–50. logh x = 3 log 2 + log, 25 - log, 20
Find x in Problems 43–50. log x + logb (x-4)= log 21
In Problems 41–46, find the equations of any vertical asymptotes. f(x) = 2 x² + x x³ - 3x² + 2x 2 3 X
Find x in Problems 43–50. log, (x + 2) + logh x = logb 24
Suppose that $2,500 is invested at 7% compounded quarterly. How much money will be in the account inCompute answers to the nearest cent. (A) 3 year? (B) 15 years?
Find x in Problems 43–50. log10(x + 6) log10 (x 3) = 1
Find x in Problems 43–50. log10 (x1) log10 (x + 1) = 1
A company manufacturing snowboards has fixed costs of $200 per day and total costs of $3,800 per day at a daily output of 20 boards. (A) Assuming that the total cost per day, C(x), is
The number of Internet hosts grew very rapidly from 1994 to 2012 (Table 5). (A) Let x represent the number of years since 1994. Find an exponential regression model (y = abx) for this data set and
What are the domain and range of the function defined by y = 1 + In(x + 1)?
Table 6 shows the life expectancy (in years) at birth for residents of the United States from 1970 to 2010. Let x represent years since 1970. Find an exponential regression model for this data and
In 2012, the estimated population in Ethiopia was 94 million people with a relative growth rate of 3.2%.(A) Write an equation that models the population growth in Ethiopia, letting 2012 be year
In its first 10 years the Gabelli Growth Fund produced an average annual return of 21.36%. Assume that money invested in this fund continues to earn 21.36% compounded annually. How long will it take
How many years (to two decimal places) will it take $1,000 to grow to $1,800 if it is invested at 6% compounded quarterly? Compounded daily?
If the world population is now 7.1 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 Problems 9–16, 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.1.5%
In Problems 9–16, 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.2.75%
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