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nature of mathematics

Questions and Answers of Nature Of Mathematics

HISTORICAL QUEST The Shroud of Turin (see Figure 10.5) is a rectangular linen cloth kept in the Chapel of the Holy Shroud in the cathedral of St. John the Baptist in Turin, Italy. It shows the image
The Arrhenius equation is used to relate the viscosity \(\eta\) of a fluid (the fluid's internal friction, which is what makes it resist a tendency to flow) to its absolute temperature \(T\)
Simplify each expression in Problems 1-4 without using a calculator or computer.Simplify each expression in Problems 1-4 without using a calculator or computer.a. \(\log 10+\ln e+\log _{2} 2 \quad
Simplify each expression in Problems 1-4 without using a calculator or computer.a. \(\log 100+\log \sqrt{10}\)b. \(\log _{2} 2^{3}+\log _{2} \sqrt{2}\)
Simplify each expression in Problems 1-4 without using a calculator or computer.a. \(\ln e+\ln 1+\ln e^{542} \quad 543\)b. \(\log _{8} 4+\log _{8} 16+\log _{8} 8^{2.3}
Simplify each expression in Problems 1-4 without using a calculator or computer.a. \(10^{\log 0.5}\)b. \(\ln e^{\log 1,000}\)
Evaluate each expression in Problems 5-8 rounded to two decimal places.a. \(\log 8.43 \quad 0.93\)b. \(\log 9,760 \quad 3.99\)
Evaluate each expression in Problems 5-8 rounded to two decimal places.a. \(\ln 2 \quad 0.69\)b. \(\ln 0.125-2.08\)
Evaluate each expression in Problems 5-8 rounded to two decimal places.a. \(\log 0.56 \quad-0.25\)b. \(\ln 26.9 \quad 3.29\)
Evaluate each expression in Problems 5-8 rounded to two decimal places.a. \(\log _{2} 10 \quad 3.32\)b. \(\log _{\pi} \frac{1}{\pi} \quad-1.00\)
Solve each equation in Problems 9-12 rounded to calculator accuracy.\(10^{x}=85 \quad 1.929418926\)
Solve each equation in Problems 9-12 rounded to calculator accuracy.\(e^{x}=500 \quad 6.214608098\)
Solve each equation in Problems 9-12 rounded to calculator accuracy.\(435^{x}=890 \quad 1.117832865\)
Solve each equation in Problems 9-12 rounded to calculator accuracy.\(e^{3 x+1}=45 \quad 0.935554163\)
Give the exact solution for each equation in Problems 13-16.a. \(\log _{6} x=4\)b. \(\log x=-3 \quad 0.001\)
Give the exact solution for each equation in Problems 13-16.a. \(2^{3 x-1}=6\)b. \(10^{2 x}=5\)
Give the exact solution for each equation in Problems 13-16.\(\log (x+1)=2+\log (x-1)\)
Give the exact solution for each equation in Problems 13-16.\(3 \ln \frac{e}{\sqrt[3]{5}}=3-\ln x \quad 5\)
Solve \(y=b^{x+1}\) for \(x \quad \log _{b} y-1\)
Solve \(A=P(1+i)^{x}\) for \(x\).
A healing law for skin wounds states that \(A=A_{0} e^{-0.1 t}\), where \(A\) is the number of square centimeters of unhealed skin after \(t\) days when the original area of the wound was \(A_{0}\).
In 1992 it was reported that the number of teenagers with AIDS doubles every 14 months. Find an equation to model the number of teenagers that may be infected over the next 10 years.
Before Hurricane Katrina in 2005, the entrance of the Aquarium of Americas in New Orleans had a gigantic building-size curve called a logarithmic spiral. Find out how to construct a logarithmic
If we assume that the world population grows exponentially, then it is also reasonable to assume that the use of some nonrenewable resource (such as petroleum) will also grow exponentially. In
In 1986 it was determined that the Challenger disaster was caused by failure of the primary O-rings. Linda Tappin gives a formula in "Analyzing Data Relating to the Disaster" (The Mathematics
Write an essay on John Napier. Include what he is famous for today and what he considered to be his crowning achievement. Also include a discussion of "Napier's bones."
Write an essay on earthquakes. In particular, discuss the Richter scale for measuring earthquakes. What is its relationship to logarithms? Footwall Hanging wall a. Normal Fault Hanging Footwall wall
Write a paper using population analysis.
From your local chamber of commerce, obtain the population figures for your city for the years \(1980,1990,2000\), and 2010. Find the rate of growth for each period. Forecast the population of your
Write an essay on carbon-14 dating. What is its relationship to logarithms? 407
A store increases its prices 10\% every odd month (January, March, May, . . .) and decreases them by \(10 \%\) every even month (February, April, June, .. .). Do prices increase, decrease, or stay
What is interest?
Contrast amount of interest and interest rate.
Compare and contrast simple and compound interest.
Compare and contrast present value and future value.
Use estimation to select the best response in Problems 5-14. Do not calculate.If you deposit \(\$ 100\) in a bank account for a year, then the amount of interest is likely to be A. \(\$ 1\)B. \(\$
Use estimation to select the best response in Problems 5-14. Do not calculate.If you deposit \(\$ 100\) in a bank account for a year, then the future value is likely to be A. \(\$ 1\)B. \(\$ 5\)C.
Use estimation to select the best response in Problems 5-14. Do not calculate.If you purchase a new automobile and finance it for four years, the amount of interest you might pay is A. \(\$ 400\)B.
Use estimation to select the best response in Problems 5-14. Do not calculate.What is a reasonable monthly income when you retire? B A. \(\$ 300\)B. \(\$ 10,000\)C. \(\$ 1,000,000\)D. impossible to
Use estimation to select the best response in Problems 5-14. Do not calculate.In order to retire and live on the interest only, what is a reasonable amount to have in the bank?A. \(\$ 300\)B. \(\$
Use estimation to select the best response in Problems 5-14. Do not calculate.If \(I=P r t\) and \(P=\$ 49,236.45, r=10.5 \%\), and \(t=2\) years, estimate \(I\).A. \(\$ 10,000\)B. \(\$ 600\)C. \(\$
Use estimation to select the best response in Problems 5-14. Do not calculate.If \(I=P r t\) and \(I=\$ 398.90, r=1.05 \%\), and \(t=1\) year, estimate \(P\).A. \(\$ 400\)B. \(\$ 40\)C. \(\$
Use estimation to select the best response. Do not calculate.If (t=3.52895), then the time is about 3 years and how many days?A. 30 B. 300 C. 52 D. 200
Use estimation to select the best response in Problems 5-14. Do not calculate.If a loan is held for 450 days, then \(t\) is about A. 450 B. 3 C. \(1 \frac{1}{4}\)D. 5
Use estimation to select the best response in Problems 5-14. Do not calculate.If a loan is held for 180 days, then \(t\) is about B A. 180 B. \(\frac{1}{2}\)C. \(\frac{1}{4}\)D. 3
In Problems 15-18, calculate the amount of simple interest earned.\(\$ 1,000\) at \(8 \%\) for 5 years \
In Problems 15-18, calculate the amount of simple interest earned.\(\$ 5,000\) at \(10 \%\) for 3 years \
In Problems 15-18, calculate the amount of simple interest earned.\(\$ 2,000\) at \(12 \%\) for 5 years
In Problems 15-18, calculate the amount of simple interest earned.\(\$ 1,000\) at \(14 \%\) for 30 years
In Problems 19-24, find the future value, using the future value formula and a calculator.\(\$ 350\) at \(4 \frac{3}{4} \%\) simple interest for 2 years
In Problems 19-24, find the future value, using the future value formula and a calculator.\(\$ 835\) at \(3.5 \%\) compounded semiannually for 6 years
In Problems 19-24, find the future value, using the future value formula and a calculator.\(\$ 575\) at \(5.5 \%\) compounded quarterly for 5 years
In Problems 19-24, find the future value, using the future value formula and a calculator.\(\$ 9,730.50\) at \(7.6 \%\) compounded monthly for 7 years
In Problems 19-24, find the future value, using the future value formula and a calculator.\(\$ 45.67\) at \(3.5 \%\) compounded daily for 3 years
In Problems 19-24, find the future value, using the future value formula and a calculator.\(\$ 119,400\) at \(7.5 \%\) compounded continuously for 30 years
In Problems 25-28, find the present value, using the present value formula and a calculator.Achieve \(\$ 5,000\) in three years at \(3.5 \%\) simple interest.
In Problems 25-28, find the present value, using the present value formula and a calculator.Achieve \(\$ 420,000\) in 30 years at \(6 \%\) interest compounded monthly.
In Problems 25-28, find the present value, using the present value formula and a calculator.Achieve a million dollars in 30 years at \(6 \%\) interest compounded continuously.
In Problems 25-28, find the present value, using the present value formula and a calculator.Achieve \(\$ 225,500\) at \(8.65 \%\) compounded continuously for 8 years, 135 days.
If \(\$ 12,000\) is invested at \(4.5 \%\) for 20 years, find the future value if the interest is compounded:a. annuallyb. semiannuallyc. quarterlyd. monthlye. dailyf. every minute g. continuously h.
If \(\$ 34,500\) is invested at \(6.9 \%\) for 30 years, find the future value if the interest is compounded:a. annuallyb. semiannuallyc. quarterlyd. monthlye. dailyf. every minute g. continuously h.
Find the total amount that must be repaid on the notes described in Problems 31-32.\(\$ 1,500\) borrowed at \(21 \%\) simple interest. What is the total amount to be repaid 55 days later?
Find the total amount that must be repaid on the notes described in Problems 31-32.\(\$ 8,553\) borrowed at \(16.5 \%\) simple interest. What is the total amount to be repaid 3 years 125 days later?
Compound interest Treasury notes authorized in 1863 and 1864 after they were purchased could be used as currency with the added bonus that they could be redeemed three years after they were issued.
Compound interest Treasury notes authorized in 1863 and 1864 after they were purchased could be used as currency with the added bonus that they could be redeemed three years after they were issued.
Compound interest Treasury notes authorized in 1863 and 1864 after they were purchased could be used as currency with the added bonus that they could be redeemed three years after they were issued.
Compound interest Treasury notes authorized in 1863 and 1864 after they were purchased could be used as currency with the added bonus that they could be redeemed three years after they were issued.
Find the cost of each item in 5 years, assuming an inflation rate of \(9 \%\).a.a. cup of coffee, \(\$ 3.75 \)b. Sunday paper, \(\$ 2.25\)c. Big Mac, \(\$ 4.10\)d. gallon of gas, \(\$ 3.95\)e. HDTV
Find the cost of each item in 10 years, assuming an inflation rate of \(5 \%\).a. movie admission, \(\$ 8.00\)b. \(\mathrm{CD}, \$ 14.95\)c. textbook, \(\$ 120.00\)d. electric bill, \(\$ 105\)e.
What is the future value after 15 years if you deposit \(\$ 1,000\) for your child's education and the interest is guaranteed at \(1.6 \%\) compounded continuously?
What is the definition of logarithm?
What is a common logarithm? What is the notation used for a common logarithm?
What is a natural logarithm? What is the notation used for natural logarithm?
Outline a procedure for solving exponential equations.
a. What does log N mean?b. What does ln N mean?c. What does logb N mean?
How do you use your calculator to evaluate the following?a. a common logarithmb. a natural logarithmc. a logarithm to a base b
What is an exponential equation?
What are the three types of exponential
Write the equations in Problems 9–12 in logarithmic form. a. 64 = 26 b. 100 10 = c. m = n
Write the equations in Problems 9–12 in logarithmic form. a. 1,000 = 10 b. 819 C. = e-
Write the equations in Problems 9–12 in logarithmic form. a. To = 10- 10 b. 36 6 = c. S = th
Write the equations in Problems 9–12 in logarithmic form. a. 125 = 5 b. 9 = ()- c. a = be
In Problems 13–18, use the definition of logarithm to simplify each expression. a. log10 10 b. log10 1,000 C. log10 10-s
In Problems 13–18, use the definition of logarithm to simplify each expression. a. log 100 b. log, 5 C. log, 25
In Problems 13–18, use the definition of logarithm to simplify each expression. a. log,5-3 b. log 0.1 C. loge
In Problems 13–18, use the definition of logarithm to simplify each expression. a. loge b. loge-4 C. log 10-3
In Problems 13–18, use the definition of logarithm to simplify each expression. - a. log, b b. log, b C. log, b-6
In Problems 13–18, use the definition of logarithm to simplify each expression. a. log 128 b. log 10" c. In en
Solve each exponential equation in Problems 19–22. Give the exact value for x. a. 4* = 1/6 c. 6 = 4.5 b. 5 = 8 d. 4* = 5
Solve each exponential equation in Problems 19–22. Give the exact value for x. a. 125 = 25 c. et = 9 b. (2)* = 5 d. = 10
Solve each exponential equation in Problems 19–22. Give the exact value for x. a. 216 = 36 c. 10 = 45 b. 10 = 2.5 d. 10 = 15
Solve each exponential equation in Problems 19–22. Give the exact value for x. a. 27 c. et = 34.2 = b. e = 1.8 d. et 6 =
Evaluate the given expressions in Problems 23–28 (to two decimal places). a. log 4.27 C. log, t b. log, b d. In 10
Evaluate the given expressions in Problems 23–28 (to two decimal places). a. log 1.08 C. log, V b. loge d. In 100
Evaluate the given expressions in Problems 23–28 (to two decimal places). a. log 71,600 c. log91 b. log39 d. In 1,000
Evaluate the given expressions in Problems 23–28 (to two decimal places). a. log 18.9 C. log, 1 b. log, 32 d. log 0.042
Evaluate the given expressions in Problems 23–28 (to two decimal places). a. In 2.27 c. In 7.3 b. In 16.77 d. In 0.321
Evaluate the given expressions in Problems 23–28 (to two decimal places). a. log e log e C. b. log e d. log 0.0532
Write each expression in Problems 29–32 in terms of common logarithms, and then give a calculator approximation (correct to four decimal places). a. log, 45 b. log,91
Write each expression in Problems 29–32 in terms of common logarithms, and then give a calculator approximation (correct to four decimal places). a. log, 10 b. log, 304

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