# Mathematics Tutors

 Subject Mathematics Due By (Pacific Time) 12/22/2016 12:00 am

 Q1. Solve the equation.log327 = x    a. {81}    b. {9}    c. {3}    d. {30}Q2. The function A = Aoe-0.0099x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 400 pounds of the material are initially put into the vault, how many pounds will be left after 40 years?    a. 350 pounds    b. 269 pounds    c. 114 pounds    d. 119 poundsQ3. The half-life of plutonium-234 is 9 hours. If 70 milligrams is present now, how much will be present in 6 days? (Round your answer to three decimal places.)    a. 0.689    b. 44.096    c. 0.001    d. 23.091Q4. The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 600 years? (Round your answer to three decimal places.)    a. 0    b. 0.286    c. 94.311    d. 55.668Q5. Change the exponential expression to an equivalent expression involving a logarithm.5x = 125    a. log125 x = 5    b. log5 125 = x    c. log125 5 = x    d. logx 125 = 5Q6. Solve for pH: pH = -log10[H+] Find the pH if the [H+] = 9.6 x 10-6.    a. 6.02    b. 5.02    c. 6.98    d. 5.98Q7. Change the exponential expression to an equivalent expression involving a logarithm.ex = 25    a. log 25 x = e    b. log x e = 25    c. ln x = 25    d. ln 25 = xQ8. Find the amount that results from the investment.\$480 invested at 16% compounded quarterly after a period of 4 years    a. \$864.45    b. \$419.03    c. \$869.11    d. \$899.03Q9. If the following defines a one-to-one function, find the inverse.{(6, 6), (12, 7), (10, 8), (8, 9)}    a. {(7, 6), (9, 10), (6, 10), (7, 8)}    b. {(7, 6), (6, 10), (6, 12), (7, 8)}    c. Not a one-to-one function    d. {(6, 6), (7, 12), (8, 10), (9, 8)}Q10. Find the effective rate of interest.50.11% compounded daily    a. 50.233%    b. 51.015%    c. 50.315%    d. 64.997%Q11. A fossilized leaf contains 12% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.    a. 1031    b. 17,099    c. 20,040    d. 36,108Q12. pH = -log10[H+] Find the [H+] if the pH = 8.4.    a. 3.98 x 10-8    b. 2.51 x 10-8    c. 3.98 x 10-9    d. 2.51 x 10-9Q13. The function f(x) = 300(0.5) x/60 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 170 years. Round to the nearest whole number.    a. 425 pounds    b. 42 pounds    c. 235 pounds    d. 53 poundsQ14. The logistic growth function f(t) =  describes the population of a species of butterflies tmonths after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months?    a. 480 butterflies    b. 401 butterflies    c. 244 butterflies    d. 4800 butterfliesQ15. A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.    a. 3.44%    b. 3.40%    c. 36%    d. 3.04%Q16. What annual rate of interest is required to triple an investment in 12 years?    a. 4.794%    b. 9.587%    c. 9.155%    d. 5.946%Q17. What principal invested at 8% compounded continuously for 4 years will yield \$1190? Round the answer to two decimal places.    a. \$864.12    b. \$1188.62    c. \$1638.78    d. \$627.48Q18. Express as a single logarithm.3log6x + 5log6(x - 6)    a. log6x3(x - 6)5    b. log6x(x - 6)15    c. log6x(x - 6)    d. 15 log6x(x - 6)Q19. If 7-x = , what does 49x equal?    a. 4    b. 16    c. -16    d. -4Q20. Express as a single logarithm.40 log5 + log5(40x6) - log5 40    a. log5 x14/5    b. log5 x14    c. log5 x13/6    d. log5 x11/8

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