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Question : Find the effective rate corresponding to the nominal rate. 6% compounded monthly : 2151548

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

Solve the problem.

1) Find the effective rate corresponding to the nominal rate. 6% compounded monthly. Round to the nearest hundredth.

A) 6.23%

B) 6.26%

C) 6.12%

D) 6.17%

2) Find the effective rate corresponding to the nominal rate. 4% compounded quarterly. Round to the nearest hundredth.

A) 4.13%

B) 4.10%

C) 4.01%

D) 4.06%

3) Find the present value of the deposit. $10,000 at 6% compounded monthly for 5 years. Round to the nearest cent.

A) $13,458.50

B) $7413.72

C) $13,488.50

D) $7443.72

4) Find the present value of the deposit. $10,000 at 4% compounded quarterly for 8 years. Round to the nearest cent.

A) $7273.04

B) $13,717.41

C) $13,749.41

D) $7305.04

5) Find the present value of the deposit. $500 at 7% compounded continuously for 10 years. Round to the nearest dollar.

A) $7240

B) $3547

C) $10,690

D) $248

6) Find the present value of the deposit. $13,000 at 4% compounded continuously for 10 years. Round to the nearest dollar.

A) $159,823

B) $542,863

C) $8714

D) $217,863

7) Barbara knows that she will need to buy a new car in 2 years. The car will cost $15,000 by then. How much should she invest now at 6%, compounded quarterly, so that she will have enough to buy a new car? Round to the nearest cent.

A) $12,594.29

B) $14,138.94

C) $13,315.67

D) $14,150.94

8) Southwest Dry Cleaners believes that it will need new equipment in 6 years. The equipment will cost $26,000. What lump sum should be invested today at 6% compounded semiannually, to yield $26,000? Round to the nearest cent.

A) $21,894.60

B) $21,731.62

C) $18,235.88

D) $23,593.24

9) An investment of $13,335 earns 9% interest compounded monthly for 4 years. (a) What is the value of the investment after 4 years? (b) If money can be deposited at 6% compounded quarterly, find the present value of the investment. Round to the nearest cent.

A) (a) $15,028.44

(b) $15,267.40

B) (a) $20,087.79

(b) $17,694.03

C) (a) $18,945.70

(b) $16,694.03

D) (a) $19,087.79

(b) $15,041.77

10) If money can be invested at 8% compounded quarterly, which is larger -- $1000 now or the present value of $1210 left at 8% interest for 7 years?

A) Present value of $1210 left for 7 years

B) $1000 now

11) A certificate of deposit pays 4% interest compounded semiannually. What effective interest rate does the CD pay? Round to the nearest tenth when necessary.

A) 2.9%

B) 8.2%

C) 4%

D) 4.7%

12) The sales of a new model of notebook computer are approximated by: S(x) = 5000 - 13,000e^{-x/9}, where x represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how many months will the sales reach $1,500,000? Round to the nearest month.

A) 12 months

B) 15 months

C) 22 months

D) 19 months

13) The sales of a mature product (one which has passed its peak) will decline by the function S(t)= S_{0}e^{-at}, where t is time in years. Find the sales after 21 years if a = 0.15 and S_{0} = 25,900. Round to the nearest sale.

A) 22,292 sales

B) 1110 sales

C) 955 sales

D) 555 sales

14) The number of books in a small library increases according to the function B = 6200e^{0.02t}, where t is measured in years. How many books will the library have after 3 years? Round to the nearest book.

A) 7575 books

B) 17,443 books

C) 7119 books

D) 6583 books

15) In the formula N = Ie^{kt}, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to double if its annual growth rate is 1.6%? Round to the nearest year.

A) 125 yr

B) 19 yr

C) 43 yr

D) 1 yr

16) In the formula N = Ie^{kt}, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to triple if its annual growth rate is 2%? Round to the nearest year.

A) 55 yr

B) 1 yr

C) 150 yr

D) 24 yr

17) In the formula N = Ie^{kt}, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. There are currently 73 million cars in a certain country, increasing by 4.4% annually. How many years will it take for this country to have 79 million cars? Round to the nearest year.

A) 3 yr

B) 2 yr

C) 41 yr

D) 1 yr

18) The number of acres in a landfill decreases according to the function B = 3800e^{-0.02t}, where t is measured in years. How many acres will the landfill have after 9 years?

A) 2511 acres

B) 3174 acres

C) 6516 acres

D) 2830 acres

19) A bacteria colony doubles in 5 hr. How long does it take the colony to triple? Use N = N_{0}2^{t/T}, where N_{0} is the initial number of bacteria and T is the time in hours it takes the colony to double. (Round to the nearest hundredth, as necessary.)

A) 15 hr

B) 7.5 hr

C) 7.92 hr

D) 2.03 hr

20) The population of a small country increases according to the function B = 2,000,000e^{0.05t}, where t is measured in years. How many people will the country have after 1 years?

A) 2,244,037 people

B) 2,102,542 people

C) 5,991,465 people

D) 2,602,060 people

21) Use the formula P = Ie^{kt}. A bacterial culture has an initial population of 10,000. If its population declines to 7000 in 6 hours, what will it be at the end of 8 hours?

A) 6215 bacteria

B) 3108 bacteria

C) 7366 bacteria

D) 1500 bacteria

22) In the formula A(t) = A_{0}e^{kt}, A(t) is the amount of radioactive material remaining from an initial amount A_{0} at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope has a half-life of approximately 800 years. How many years would be required for a given amount of this isotope to decay to 75% of that amount?

A) 1600 yr

B) 332 yr

C) 257 yr

D) 200 yr

23) In the formula A(t) = A_{0}e^{kt}, A(t) is the amount of radioactive material remaining from an initial amount A_{0} at a given time t and k is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 48% of the carbon-14 it originally contained, what is the approximate age of the artifact, rounded to the nearest year? (carbon-14 decays at the rate of 0.0125% annually.)

A) 2550 yr

B) 5872 yr

C) 4160 yr

D) 3840 yr

24) In the formula A(t) = A_{0}e^{kt}, A(t) is the amount of radioactive material remaining from an initial amount A_{0} at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this isotope, to the nearest year.

A) 4 yr

B) 172 yr

C) 286 yr

D) 396 yr

25) The amount of particulate matter left in solution during a filtering process decreases by the equation P = 1000(2)^{-0.8n}, where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

A) 1000, 16,000

B) 1000, 63

C) 2000, 63

D) 1000, 31

26) The decay of 336 mg of an isotope is given by A(t)= 336e^{-0.015t}, where t is time in years. Find the amount left after 53 years.

A) 149 mg

B) 76 mg

C) 152 mg

D) 331 mg

27) Newton's law of cooling states that the temperature f(t) of a body at time t is given by: f(t) = T_{0} + Ce^{-kt}, where C and k are constants and T_{0} is the temperature of the environment in which the object rests. If

C = -26.7 and k = 0.06 and t is in hours, how long will it take for a frozen roast to thaw to a temperature of 0°C in a refrigerator that is at 5°C? Round your answer to the nearest hour.

A) 22 hr

B) 26 hr

C) 28 hr

D) 32 hr

28) Newton's law of cooling states that the temperature f(t) of a body at time t is given by: f(t) = T_{0} + Ce^{-kt}, where C and k are constants and T_{0} is the temperature of the environment in which the object rests. If

C = 280 and k = 0.18 and t is in minutes, how long will it take for a glass baking dish containing brownies to cool to a comfortable-to-touch temperature of 95°F in a room that is at 69°F? Round your answer to the nearest minute.

A) 10 min

B) 8 min

C) 17 min

D) 13 min

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

Provide an appropriate response.

29) The graph of y = f(x) has an x-intercept of a and a y-intercept of b. What are the intercepts of the graph of y = f(-x)?

30) A classmate claims that, if a function f(x) has a horizontal asymptote at y = w, then the function can only approach w but cannot actually equal w. Evaluate the classmate's claim.

31) Suppose the population of deer fluctuates over time. The population increases in the summer and decreases in the winter. It also varies over many years as well. If you looked at the graph of population versus time, would this relation be a function? Why or why not?

32) Consider the linear function f(x) = 5x + 20. What is the domain and range of this function? Now, suppose the function represents the relationship between studying time and grades on an exam. The variable x represents the number of hours spent studying and f(x) represents the grade on the exam. Does this change the domain and range? If so, what is the new domain and range and why is it different?

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

33) True or False. The function y = (x^{2} - 52/x - 5) is not continuous at x = 5.

A) False

B) True

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

34) f(x) = ax

The graph of an exponential function with base a is given. Sketch the graph of g(x) = -ax. Give the domain and range of g.

35) f(x) = ax

The graph of an exponential function with base a is given. Sketch the graph of h(x) = a-x. Give the domain and range of h.

36) Explain how the graph of y = 3x + 5 - 1 can be obtained from the graph of y = 3x.

37) Explain how the graph of y = (1/3)^{x} + 3 can be obtained from the graph of y = 3x.