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Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M3 ALGEBRA II Problem Set 1. 2. 3. 4. Solve each of the following equations for π₯ using the same technique as was used in the Opening Exercise. a. 2π₯ = 32 b. 2π₯β3 = 22π₯+5 c. 2π₯ 2 β3π₯ = 2β2 d. 2π₯ β 24π₯β3 = 0 e. 23π₯ β 25 = 27 f. 2π₯ 2 β16 =1 32π₯ = 27 h. 3π₯ = 81 3π₯ 2 g. 2 Solve the equation 22π₯ 2π₯+5 i. 35π₯ = 36 = 1 algebraically using two different initial steps as directed below. a. Write each side as a power of 2. b. Multiply both sides by 2π₯+5 . Find consecutive integers that are under and over estimates of the solutions to the following exponential equations. a. 2π₯ = 20 b. 2π₯ = 100 c. 3π₯ = 50 d. 10π₯ = 432,901 e. 2π₯β2 = 750 f. 2π₯ = 1.35 Complete the following table to approximate the solution to 10π₯ = 34,198 to three decimal places. π πππ π πππ 1 10 4.1 4.51 4.531 2 100 4.2 4.52 4.532 3 1,000 4.3 4.53 4.533 4 10,000 4.4 4.54 4.534 5 100,000 4.5 π πππ π πππ 4.535 4.6 Lesson 7: Bacteria and Exponential Growth This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG II-M3-TE-1.3.0-08.2015 S.47 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M3 ALGEBRA II 5. Complete the following table to approximate the solution to 2π₯ = 19 to three decimal places. π ππ π ππ π ππ π ππ 6. Approximate the solution to 5π₯ = 5,555 to four decimal places. 7. A dangerous bacterial compound forms in a closed environment but is immediately detected. An initial detection reading suggests the concentration of bacteria in the closed environment is one percent of the fatal exposure level. This bacteria is known to double in concentration in a closed environment every hour and can be modeled by the function π(π‘) = 100 β 2π‘ , where π‘ is measured in hours. a. In the function π(π‘) = 100 β 2π‘ , what does the 100 mean? What does the 2 mean? b. Doctors and toxicology professionals estimate that exposure to two-thirds of the bacteriaβs fatal concentration level will begin to cause sickness. Without consulting a calculator or other technology, offer a rough time limit for the inhabitants of the infected environment to evacuate in order to avoid sickness. c. A more conservative approach is to evacuate the infected environment before bacteria concentration levels reach one-third of fatal levels. Without consulting a calculator or other technology, offer a rough time limit for evacuation in this circumstance. Lesson 7: Bacteria and Exponential Growth This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG II-M3-TE-1.3.0-08.2015 S.48 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M3 ALGEBRA II d. π Use the method of the example to approximate when the bacteria concentration will reach 100% of the fatal exposure level, to the nearest minute. ππ π Lesson 7: ππ π Bacteria and Exponential Growth This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG II-M3-TE-1.3.0-08.2015 ππ π ππ π ππ S.49 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
