MAC 1105 Chapter 6 (6.5 to 6.8) --Sullivan 8th Ed Name: Practice for the Exam Kincade

Size: px

Start display at page:

Download "MAC 1105 Chapter 6 (6.5 to 6.8) --Sullivan 8th Ed Name: Practice for the Exam Kincade"

Derick Chase
5 years ago
Views:

1 MAC 05 Chapter 6 (6.5 to 6.8) --Sullivan 8th Ed Name: Practice for the Eam Date: Kincade MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the properties of logarithms to find the eact value of the epression. Do not use a calculator. ) ln e A) B) 4 C) e D) 6 ) ) log log70 7 A) 7 B) C) 0 D) 70 3) log5 4 log4 5 A) 4 B) 5 C) 5 D) 3 ) 3) 4) eln 8 A) 7 B) ln 8 C) e8 D) 8 4) 5) e log e 00 A) e0 B) e00 C) 0 D) 00 5) Suppose that ln = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 6) ln 3 A) 0a B) ab C) 5a D) a5 6) 7) ln 6 0 A) 6 (a + b) B) 3 (a - b) C) 3 (a + b) D) 6 (a + b) 7) Write as the sum and/or difference of logarithms. Epress powers as factors. 8) log 7 m n 8) A) log (7 m) - log n B) log 7 + log m - log n C) log 7 log m log n D) log n - log 7 - log m 9) log A) 7log 6 -log 6 ( - 4) B) log 6 ( - 4) - 7log 6 C) log 6 ( - 4) -log 6 D) log 6 ( - 4) + 7log 6 9)

2 0) ln 5 ey 0) A) y 5 B) 5 ln y + 5 C) 5 ln 5 ey + 5 D) 5 ln y ) log 9 y ) A) 7 log log 9 y - log 9 B) 7 log log 9 y - log 9 7 C) log log 9 y - log 9 D) 7 log log 9 y - log 9 Epress as a single logarithm. ) log b t - log b s A) log b t log b s B) log b t s C) log b t s D) log b (t - s) ) 3) 6ln ( - 3) - 5 ln A) ln ( - 3) 6 5 B) ln 30( - 3) C) ln 6( - 3) 5 D) ln 5( - 3)6 3) 4) log + log ( - 6) - log 5 - log (- 4) ( - 6)( - 4) A) log 5 C) log ( - 6) 5( - 4) B) log D) log ( + 4) 5 + 4) 9-4) 5) 4 log log 5 ( - 4) - log 5 5) A) log B) log5 5-4 C) log D) log Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 6) log 84 6) 5.8 A).94 B).5 C) D) ) log A) B) 3.55 C) 0.54 D) )

3 Solve the equation. 8) log 4 ( + ) = 3 A) {8} B) {65} C) {80} D) {63} 8) 9) log (5 + ) - log ( - 3) = log 5 A) {-5} B) {5} C) 3 D) 9) 0) log 4 ( + 4) = 4 + log 4 ( - ) A) B) 5 C) 5 5 D) - 5 0) Solve the equation. Epress irrational answers in eact form and as a decimal rounded to 3 decimal places. ) ln + ln ( + 5) = -4 A) e B) e -4 C) e D) e ) Solve the problem. ) f() = log( + 3) and g() = log( - ). Solve f() = 3. What point is on the graph of f? A) {6}, (4, 7) B) {6}, (4, 3) C) {4}, (4, 9) D) {4}, (4, 3) 3) The ph of a solution ranges from 0 to 4. 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 where represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration if the ph = 4. A) 0.5 B) 0-4 C).39 D) 04 ) 3) Solve the equation. 4) log3 + log3( - 4) = 4 A) {-3, 7} B) {7} C) {53} D) 4) 5) 4( + ) = 64 A) {4} B) {} C) {6} D) {-} 5) 6) (7 + 3) = 4 6) A) {} B) {3} C) {-3} D) 7) 3 5t - = 75 3 A) B) C) 3 0 D) {3} 7) 3

4 Use a graphing calculator to solve the equation. Round your answer to two decimal places. 8) log4( + ) - log5( - ) = A) {.05} B) {-0.69} C) {.75} D) {.00} 8) Find the amount that results from the investment. 9) $480 invested at % compounded quarterly after a period of 7 years A) $68. B) $066. C) $06.3 D) $098. 9) 30) $,000 invested at 7% compounded quarterly after a period of 3 years A) $4,700.5 B) $4,777.7 C) $4,53. D) $ ) Find the effective rate of interest. 3) 8.75% compounded monthly A) 9.% B) 9.655% C) 8.955% D) 8.873% 3) Find the present value. Round to the nearest cent. 3) To get $0,500 after 4 years at 9% compounded annually A) $ B) $ C) $ D) $ ) 33) To get $0,000 after 3 years at 6% compounded monthly A) $0,66.78 B) $ C) $ D) $ ) Solve the problem. 34) How much money needs to be invested now to get $000 after 4 years at 8% compounded quarterly? Epress your answer to the nearest dollar. A) $457 B) $584 C) $746 D) $848 34) Solve the problem. Round your answer to three decimals. 35) What annual rate of interest is required to triple an investment in years? A) 9.55% B) 4.794% C) 9.587% D) 5.946% 35) 36) How long will it take for an investment to triple in value if it earns 7.5% compounded continuously? A) 9.56 yr B) yr C) 5.53 yr D) 6.36 yr 36) Solve the problem. 37) The population of a particular country was 5 million in 98; in 996, it was 3 million. The eponential growth function A = 5ekt describes the population of this country t years after 98. Use the fact that 5 years after 98 the population increased by 6 million to find k to three decimal places. A) 0.04 B) 0.04 C) D) ) 38) How long will it take for the population of a certain country to double if its annual growth rate is 3.5%? Round to the nearest year. A) 57 yr B) 0 yr C) 9 yr D) yr 38) 39) The population of a small country increases according to the function B = 900,000e0.05t, where t is measured in years. How many people will the country have after 4 years? A),448,494 B),46,404 C) 69,073 D),099,6 39) 4

5 40) The half-life of plutonium-34 is 9 hours. If 40 milligrams is present now, how much will be present in 5 days? (Round your answer to three decimal places.) A) 7.5 B) C) D) ) 4) The function A = A0e models the amount in pounds of a particular radioactive material stored in a concrete vault, where is the number of years since the material was put into the vault. If 800 pounds of the material are initially put into the vault, how many pounds will be left after 80 years? A) 33 lb B) 635 lb C) 00 lb D) 00 lb 4) 4) Sandy manages a ceramics shop and uses a 600 F kiln to fire ceramic greenware. After turning off her kiln, she must wait until its temperature gauge reaches 65 F before opening it and removing the ceramic pieces. If room temperature is 80 F and the gauge reads 450 F in 4 minutes, how long must she wait before opening the kiln? Assume the kiln cools according to Newton's Law of Cooling: U = T + (U0 - T)ekt. (Round your answer to the nearest whole minute.) A) min B) 75 min C) 57 min D) 75 min 4) 43) The logistic growth model P(t) = 000 represents the population of a bacterium in a + 9e-0.358t culture tube after t hours. When will the amount of bacteria be 60? A) 9.59 hr B).3 hr C) 4.0 hr D) 6.89 hr 43) 44) The logistic growth model P(t) = represents the proportion of the total market of a e-0.877t new product as it penetrates the market t years after introduction. When will the product have 65% of the market? A).5 yr B).3 yr C).3 yr D) 3.5 yr 44) Find the effective rate of interest. 45) 6.5% compounded quarterly A) 6.455% B) 6.373% C) 7.55% D) 6.398% 45) Solve the equation. 46) 45-3 = 56 46) A) {-3} B) {8} C) 64 D) {3} 47) 3(3-6 ) = 7 A) {-3} B) 9 C) {9} D) {3} 47) 5

6 48) 4- = 6 48) A) {} B) C) {-} D) 4 49) - 3 = 64 A) {3} B) {6} C) {3, -3} D) { 35, - 35} 49) 50) 9 7(3 - ) = 9 50) A) {-8} B) {-} C) {0} D) ,

7 Answer Key Testname: MAC 05 CHAPTER 6 (6.5 TO 6.8) PRACTICE FOR THE TEST ) A ) B 3) D 4) D 5) C 6) C 7) A 8) B 9) B 0) D ) A ) C 3) A 4) B 5) C 6) B 7) D 8) D 9) B 0) C ) B ) D 3) B 4) B 5) B 6) C 7) A 8) D 9) D 30) B 3) A 3) C 33) C 34) A 35) C 36) C 37) A 38) B 39) D 40) B 4) C 4) D 43) A 44) A 45) D 46) D 47) D 48) A 49) C 50) B 7

6.2 Indicate whether the function is one-to-one. 16) {(-13, -20), (-10, -20), (13, -8)}

6.2 Indicate whether the function is one-to-one. 16) {(-13, -20), (-10, -20), (13, -8)} Math 0 Eam Review. Evaluate the epression using the values given in the table. ) (f g)() 7 f() - - - g() - 7 Evaluate the epression using the graphs of = f() and = g(). ) Evaluate (fg)(). 9) H() = - 7