precalculus

QUIZ 3 Professor: Ms. Chowdhury MATH 115 Fall 2018 Name___________________________________ Date ________________ INSTRUCTIONS

The quiz is worth 55 points. There are 20 multiple choice (2 points) and 5 (3 points) short answer problems.

This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone.

You must show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit at the discretion of the professor.

Please type your answers on the table in the separate answer sheet.Scanned handwritten work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module.

If you have any questions, please contact me by e-mail.

Please record your answer in the table below.

I have completed this assignment myself, working independently and not consulting anyone except the instructor and my notes. (If this part is not completed, you will receive a zero for the quiz)

Sign here __________________________________________ Date _______________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) ( log a t - log a s) + 6 log a u

A) log a t

u6s B) log a tu

6s C) log a 6tu

s D) log a

tu6 s

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2) 5 log3 2 + 1 5

log3 (r - 2) - 1 2

log3 r

A) log3 5r - 10

10r B) log3

32 5

r - 2 r

C) log3 32r - 2

10r D) log3

1 2

r - 2 r

Solve the equation by expressing each side as a power of the same base and then equating exponents.

3) 3(6 - 3x) = 127

A) {3} B) {-3} C) {9} D) {19 }

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

4) 7x = 6x + 7

A) 81.36 B) 42.00 C) 40.68 D) 3.36

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

5) log 21 (x + 84) = 3 - log 21 x

A) {147} B) {-63} C) {63} D) {-147}

6) ln x + ln (x -1) = ln 6

A) {3} B) {-2} C) 72 D) {3, -2}

7) log4 (x + 4) - log4 (x - 2) = 3

A) {- 4421 } B) {4421

} C) { 221 } D)

8) ln (x - 9) - ln (x + 6) = ln (x - 5) - ln (x + 2)

A) B) 6 C) 32 D) -

6 5

9) 6 + 8 ln x = 15

A) 98 ln 1 B) e 9/8 C) ln 98 D)

e9 8

Solve the problem.

10) If Emery has $2300 to invest at 10% per year compounded monthly, how long will it be before he has $3200? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.)

A) 61.12 yrs, 3.502 yrs B) 0.289 yrs, 0.275 yrs

C) 3.159 yrs, 0.33 yrs D) 3.316 yrs, 3.302 yrs

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11) Find out how long it takes a $3300 investment to double if it is invested at 7% compounded semiannually.

Round to the nearest tenth of a year. Use the formula A = P 1 + r n

nt .

A) 10.5 years B) 10.3 years C) 10.1 years D) 9.9 years

12) The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = - log x where x represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration if the pH = 6.4.

A) 3.98 x 10-6 B) 2.51 x 10-7 C) 2.51 x 10-6 D) 3.98 x 10-7

Solve.

13) The function A = A0e-0.01155x 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 600 pounds of the material are placed in the vault, how much time will need to pass for only 267 pounds to remain?

A) 70 years B) 140 years C) 80 years D) 75 years

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places

14) log 17

A) 0.7333 B) 0.4040 C) 1.7276 D) 2.4750

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

15) ln e 5 9

A) 5 + ln 9 B) ln e5 - ln 9 C) ln e5 + ln 9 D) 5 - ln 9

16) loga x4

3 x + 5

(x -2)2

A) loga x4 + loga (x + 5)-3 - loga (x - 2)2 B) 4 loga x - 3 loga (x + 5) - 2 loga ( x - 2)

C) loga x4 + loga (x + 5)1/3 - loga (x - 2)2 D) 4 loga x + 1 3

loga (x + 5) - 2 loga (x - 2)

17) log 2x 4 5 3 - x

6(x + 3)2

A) log (2x4 5

3 - x) - log (6(x + 3)2)

B) log 2 + log x4 + log (3 - x)1/5 - log 6 - log (x + 3)2

C) log 2 + 4log x + 15 log (3 - x) - log 6 - 2log (x + 3)

D) log 2 + 4log x + 15 log (3 - x) - log 6 + 2log (x + 3)

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18) log 5 7

y

A) 1 7

log 5 7

y B) 15 log 7 y C)

1 7

log 5 y D) 7 log 5 y

19) log x10,000

A) log x + 4 B) 10,000x C) -40x D) log x - 4

20) log (10,000x)

A) 4 + log x B) 4log x C) 40 + log x D) 4x

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Present data in the form of tables. For each data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data.

21) Percentage of Population Living in the South Suburbs of a Large City

Year Percent 1950 55 1960 69 1970 74 1980 76 2000 76

Solve the exponential equation. Express the solution set in terms of natural logarithms.

22) 4x + 4 = 52x + 5

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

23) e2x + ex - 6 = 0

Solve the problem.

24) The formula A = 106e0.032t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 120 thousand?

25) The population of a particular country was 23 million in 1984; in 1992, it was 32 million. The exponential growth function A =23ekt describes the population of this country t years after 1984. Use the fact that 8 years after 1984 the population increased by 9 million to find k to three decimal places.

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