# Exam: 250310RR

Exam: 250310RR - Exponents, Logarithms, Sequences, and Series

1. Write the equation below in its equivalent logarithmic form:

2. Compute the value of

A. 0.0088

B. 109.95

C. 290.54

D. 181.59

3. Let an be a sequence defined by the recursion formulas a first three terms of the sequence a

A. 4, 16, 20922789887968

B. 4, 8, 4784

C. 4, 8, 40064

D. 4, 16, 64

4. Find the accumulated value of an investment of $7,000 at 7% compounded continuously for 6 years.

Solve this question using the correct formula for compound interest.

A. $10,653.73

B. $10,753.73

C. $10,505.11

D. $9,940.00

5. Use properties of logarithms to expand the logarithmic expression below as much as possible.

A. ln e

5

7. Which of the following statements is not correct?

A. Mathematical induction proves facts about all positive real numbers.

B. Mathematical induction involves first proving a statement S1 and then proving a second statement, that S

C. Mathematical induction is a method of proof.

D. A necessary skill to master before attempting a proof by mathematical induction is the ability to write three forms of a statement, S

8. Write the first five terms of the arithmetic sequence below.

A. 19, 15, 11, 7, 3

B. 11, 7, 3, - 1, - 5

C. 15, 11, 7, 3, - 1

D. 15, 11, 6, 3, - 1

9. Write the first four terms of the sequence whose general term is given by the following formula:

A.- 3, - 7, - 11, - 15

B. 5, 9, 13, 17

C. 3, 4, 5, 6

D. 3, 7, 11, 15

10. Which of these is not a valid fact about logarithms?

11. What type of transformation would occur with the following exponential functions?

A. Reflection about the x-axis

B. Vertical shrinking

C. Reflection about the y-axis

D. Vertical stretching

12. Make a table of coordinates for the function below and then graph it.

13. Find the first five terms of the arithmetic sequence in which a

A. 6, 5, 4, 3, 2

B. 6, 5, 3, 3, 2

C. 5, 4, 3, 2, 1

D. 7, 6, 5, 4, 3

14. Use properties of logarithms to condense the logarithmic expression below to one term whose coefficient is 1.

15. Solve the logarithmic equation below. Be sure to reject any value that isn't in the domain of the original logarithmic expressions. Give the exact answer.

16. Find the sum of the first 60 terms of the arithmetic sequence 14, 19, 24, 29, .

A. 9,700

B. 9,840

C. 9,690

D. 314

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

18. Find the common ratio of the geometric sequence given below.

19. Your textbook suggests that the percent risk R of an auto accident can be modeled by the formula 6e12.77x, where x stands for blood alcohol concentration. At what blood alcohol concentration is a driver 50% likely to have an accident?

A. 0.166

B. 0.072

C. 3557

D. 0.427

20. Evaluate the expression below without using a calculator.

1. Write the equation below in its equivalent logarithmic form:

2. Compute the value of

A. 0.0088

B. 109.95

C. 290.54

D. 181.59

3. Let an be a sequence defined by the recursion formulas a first three terms of the sequence a

A. 4, 16, 20922789887968

B. 4, 8, 4784

C. 4, 8, 40064

D. 4, 16, 64

4. Find the accumulated value of an investment of $7,000 at 7% compounded continuously for 6 years.

Solve this question using the correct formula for compound interest.

A. $10,653.73

B. $10,753.73

C. $10,505.11

D. $9,940.00

5. Use properties of logarithms to expand the logarithmic expression below as much as possible.

A. ln e

5

7. Which of the following statements is not correct?

A. Mathematical induction proves facts about all positive real numbers.

B. Mathematical induction involves first proving a statement S1 and then proving a second statement, that S

C. Mathematical induction is a method of proof.

D. A necessary skill to master before attempting a proof by mathematical induction is the ability to write three forms of a statement, S

8. Write the first five terms of the arithmetic sequence below.

A. 19, 15, 11, 7, 3

B. 11, 7, 3, - 1, - 5

C. 15, 11, 7, 3, - 1

D. 15, 11, 6, 3, - 1

9. Write the first four terms of the sequence whose general term is given by the following formula:

A.- 3, - 7, - 11, - 15

B. 5, 9, 13, 17

C. 3, 4, 5, 6

D. 3, 7, 11, 15

10. Which of these is not a valid fact about logarithms?

11. What type of transformation would occur with the following exponential functions?

A. Reflection about the x-axis

B. Vertical shrinking

C. Reflection about the y-axis

D. Vertical stretching

12. Make a table of coordinates for the function below and then graph it.

13. Find the first five terms of the arithmetic sequence in which a

A. 6, 5, 4, 3, 2

B. 6, 5, 3, 3, 2

C. 5, 4, 3, 2, 1

D. 7, 6, 5, 4, 3

14. Use properties of logarithms to condense the logarithmic expression below to one term whose coefficient is 1.

15. Solve the logarithmic equation below. Be sure to reject any value that isn't in the domain of the original logarithmic expressions. Give the exact answer.

16. Find the sum of the first 60 terms of the arithmetic sequence 14, 19, 24, 29, .

A. 9,700

B. 9,840

C. 9,690

D. 314

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

18. Find the common ratio of the geometric sequence given below.

19. Your textbook suggests that the percent risk R of an auto accident can be modeled by the formula 6e12.77x, where x stands for blood alcohol concentration. At what blood alcohol concentration is a driver 50% likely to have an accident?

A. 0.166

B. 0.072

C. 3557

D. 0.427

20. Evaluate the expression below without using a calculator.

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