Algebra 2 (Standard) DIA #6
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1 Name: Class: Date: Algebra 2 (Standard) DIA #6 Multiple Choice Identify the choice that best completes the statement or answers the question.. An initial population of 865 quail increases at an annual rate of 3%. Write an exponential function to model the quail population. What will the approximate population be after 2 years? a. f(x) 865(3) x ; 83,265 c. f(x) x ; 7,90 b. f(x) 865(0.3) x ; 8 d. f(x) 865(.3) x ; 8 Graph the function. 2. y 7 x 3 a. c. b. d.
2 Name: 3. y 7 x 6 a. c. b. d. 2
3 Name:. y 05 x 2 a. c. b. d. 5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 787 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 6 hours. Round your answer to the nearest thousandth. a. y x 78 x 2 ; kg c. y ; kg b. y 78 x ; 0.27 kg d. y x 2 ; 0 kg 6. Suppose you invest $600 at an annual interest rate of.6% compounded continuously. How much will you have in the account after 0 years? a. $2,53.52 b. $25,35.8 c. $2, d. $6,
4 Name: Write the equation in logarithmic form a. log c. log b. log d. log Evaluate the logarithm. 8. log 6 a. b. 2 c. 2 d. 9. log 2 6 a. 5 b. 6 c. 6 d. 2 Write the expression as a single logarithm log b w 6 log b q a. log b (w 5 q 6 ) c. log b wq 5 6 b. log b w 5 q 6 d. 5 6 log b w q. log 2 5 log 2 9 a. log 5 b. log 6 c. log 2 5 d. log 2 6 Expand the logarithmic expression. b 2. log 9 a. log 9 b log 9 c. b log 9 b. log 9 b log 9 d. log 9 log 9 b 3. log 9 6d a. log 9 6 log 9 d c. log 9 6 log 9 d b. log 9 6 log 9 d d. 6 log 9 d. Use the Change of Base Formula to evaluate log a..0 c..0 b..929 d Use the Change of Base Formula to evaluate log 6 8. a..39 c..908 b d. 2.53
5 Name: 6. What is the value of log 256? a. c. 256 b. d A company with loud machinery needs to cut its sound intensity to 55% of its original level. By how many decibels would the loudness be reduced? Use the formula L 0 log I. Round to the nearest hundredth. I o a decibels c..90 decibels b. 3.7 decibels d..6 decibels Solve the exponential equation x 8 a. 36 b. 9 c. 2 7 d Solve 2 7x 96. Round to the nearest ten-thousandth. a b c d Use a table to solve. Round to the nearest hundredth x 2 a..80 b..6 c d Use a graphing calculator. Solve 5 3x 665 by graphing. Round to the nearest hundredth. a..5 b c..07 d The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria t increase in population is shown by the formula G, where t is the time period of the population 3.3 log a P increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is.5 hours, how long will it take 9 of these bacteria to multiply into a colony of 792 bacteria? Round to the nearest hour. a. 57 hours b. 60 hours c. 33 hours d. 3 hours Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary. 23. Solve log(8x 2). a. b. 8 c. 5 d Solve log 2x log 3 0. Round to the nearest hundredth if necessary. a..5 b. 6 c. 0.7 d
6 Algebra 2 (Standard) DIA #6 Answer Section MULTIPLE CHOICE. ANS: D PTS: DIF: L3 REF: 7- Exploring Exponential Models OBJ: 7-. To model exponential growth and decay STA: MA.92.A.8. MA.92.A.8.3 MA.92.A.8.7 TOP: 7- Problem 3 Modeling Exponential Growth KEY: exponential growth exponential function DOK: DOK 3 2. ANS: A PTS: DIF: L3 OBJ: 7-2. To explore the properties of functions of the form y = ab^x STA: MA.92.A.2.5 MA.92.A.2.0 MA.92.A.8. MA.92.A.8.3 MA.92.A.8.7 TOP: 7-2 Problem Graphing y = ab^x KEY: exponential function 3. ANS: C PTS: DIF: L3 OBJ: 7-2. To explore the properties of functions of the form y = ab^x STA: MA.92.A.2.5 MA.92.A.2.0 MA.92.A.8. MA.92.A.8.3 MA.92.A.8.7 TOP: 7-2 Problem 2 Translating y = ab^x KEY: exponential function. ANS: B PTS: DIF: L OBJ: 7-2. To explore the properties of functions of the form y = ab^x STA: MA.92.A.2.5 MA.92.A.2.0 MA.92.A.8. MA.92.A.8.3 MA.92.A.8.7 TOP: 7-2 Problem 2 Translating y = ab^x KEY: exponential function 5. ANS: A PTS: DIF: L3 OBJ: 7-2. To explore the properties of functions of the form y = ab^x STA: MA.92.A.2.5 MA.92.A.2.0 MA.92.A.8. MA.92.A.8.3 MA.92.A.8.7 TOP: 7-2 Problem 3 Using an Exponential Model KEY: exponential function DOK: DOK 3 6. ANS: A PTS: DIF: L2 OBJ: To graph exponential functions that have base e STA: MA.92.A.2.5 MA.92.A.2.0 MA.92.A.8. MA.92.A.8.3 MA.92.A.8.7 TOP: 7-2 Problem 5 Continuously Compounded Interest KEY: continuously compounded interest 7. ANS: A PTS: DIF: L2 REF: 7-3 Logarithmic Functions as Inverses OBJ: 7-3. To write and evaluate logarithmic expressions STA: MA.92.A.2.5 MA.92.A.2. MA.92.A.8. MA.92.A.8.3 TOP: 7-3 Problem Writing Exponential Equations in Logarithmic Form KEY: logarithm
7 8. ANS: B PTS: DIF: L3 REF: 7-3 Logarithmic Functions as Inverses OBJ: 7-3. To write and evaluate logarithmic expressions STA: MA.92.A.2.5 MA.92.A.2. MA.92.A.8. MA.92.A.8.3 TOP: 7-3 Problem 2 Evaluating a Logarithm KEY: logarithm 9. ANS: C PTS: DIF: L2 REF: 7-3 Logarithmic Functions as Inverses OBJ: 7-3. To write and evaluate logarithmic expressions STA: MA.92.A.2.5 MA.92.A.2. MA.92.A.8. MA.92.A.8.3 TOP: 7-3 Problem 2 Evaluating a Logarithm KEY: logarithm 0. ANS: A PTS: DIF: L3 REF: 7- Properties of Logarithms TOP: 7- Problem Simplifying Logarithms. ANS: D PTS: DIF: L2 REF: 7- Properties of Logarithms TOP: 7- Problem Simplifying Logarithms 2. ANS: A PTS: DIF: L2 REF: 7- Properties of Logarithms TOP: 7- Problem 2 Expanding Logarithms 3. ANS: B PTS: DIF: L3 REF: 7- Properties of Logarithms TOP: 7- Problem 2 Expanding Logarithms. ANS: C PTS: DIF: L2 REF: 7- Properties of Logarithms TOP: 7- Problem 3 Using the Change of Base Formula KEY: Change of Base Formula 5. ANS: B PTS: DIF: L3 REF: 7- Properties of Logarithms TOP: 7- Problem 3 Using the Change of Base Formula KEY: Change of Base Formula 6. ANS: D PTS: DIF: L2 REF: 7- Properties of Logarithms TOP: 7- Problem 3 Using the Change of Base Formula KEY: Change of Base Formula 7. ANS: A PTS: DIF: L3 REF: 7- Properties of Logarithms TOP: 7- Problem Using a Logarithmic Scale KEY: properties of logarithms problem solving 8. ANS: C PTS: DIF: L2 OBJ: 7-5. To solve exponential and logarithmic equations STA: MA.92.A.8.5 TOP: 7-5 Problem Solving an Exponential Equation Common Base KEY: exponential equation 2
8 9. ANS: D PTS: DIF: L3 OBJ: 7-5. To solve exponential and logarithmic equations STA: MA.92.A.8.5 TOP: 7-5 Problem 2 Solving an Exponential Equation Different Bases KEY: exponential equation 20. ANS: C PTS: DIF: L2 OBJ: 7-5. To solve exponential and logarithmic equations STA: MA.92.A.8.5 TOP: 7-5 Problem 3 Solving an Exponential Equation With Graph or Table KEY: exponential equation 2. ANS: A PTS: DIF: L3 OBJ: 7-5. To solve exponential and logarithmic equations STA: MA.92.A.8.5 TOP: 7-5 Problem 3 Solving an Exponential Equation With Graph or Table KEY: exponential equation 22. ANS: B PTS: DIF: L OBJ: 7-5. To solve exponential and logarithmic equations STA: MA.92.A.8.5 TOP: 7-5 Problem Modeling With an Exponential Equation KEY: logarithmic equation DOK: DOK ANS: B PTS: DIF: L3 OBJ: 7-5. To solve exponential and logarithmic equations STA: MA.92.A.8.5 TOP: 7-5 Problem 5 Solving a Logarithmic Equation KEY: logarithmic equation 2. ANS: C PTS: DIF: L3 OBJ: 7-5. To solve exponential and logarithmic equations STA: MA.92.A.8.5 TOP: 7-5 Problem 6 Using Logarithmic Properties to Solve an Equation KEY: logarithmic equation 3
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