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ELF.01.8 – Solving Word Problems Using Logarithms MCB4U - Santowski

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(A) Examples The logarithmic function has applications for solving everyday situations: ex 1. Mr. S. drinks a cup of coffee at 9:45 am and his coffee contains 150 mg of caffeine. Since the half-life of caffeine for an average adult is 5.5 hours, determine how much caffeine is in Mr. S.'s body at class-time (1:10pm). Then determine how much time passes before I have 30 mg of caffeine in my body. ex 2. The value of the Canadian dollar, at a time of inflation, decreases by 10% each year. What is the half- life of the Canadian dollar?

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(A) Examples ex 3. The half-life of radium-226 is 1620 a. Starting with a sample of 120 mg, after how many years is only 40 mg left? ex 4. Find the length of time required for an investment of $1000 to grow to $4,500 at a rate of 9% p.a. compounded quarterly.

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(A) Examples ex 5. Dry cleaners use a cleaning fluid that is purified by evaporation and condensation after each cleaning cycle. Every time it is purified, 2% of the fluid is lost (a) An equipment manufacturer claims that after 20 cycles, about two-thirds of the fluid remains. Verify or reject this claim. (b) If the fluid has to be "topped up" when half the original amount remains, after how many cycles should the fluid be topped up? (c) A manufacturer has developed a new process such that two-thirds of the cleaning fluid remains after 40 cycles. What percentage of fluid is lost after each cycle?

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(B) Examples with Data Analysis Given the following data of numbers of bacteria: (i) use graphing technology to graph the data (ii) use graphing technology to determine a reasonable regression equation for an algebraic model of the data (iii) using your equation, how many bacteria would you expect in 9 days? (iv) what is the doubling period of the bacteria? (v) how long does it take to get 2000 bacteria? Day01234 # of bacteria 300378476600756

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(B) Homework Nelson Text, p132, Q11-16 Nelson Text, p153, Q4-8,11,12 Photocopy page 100-101 from Houghton Math 12

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Section 4.2 Logarithms and Exponential Models. The half-life of a substance is the amount of time it takes for a decreasing exponential function to decay.

Section 4.2 Logarithms and Exponential Models. The half-life of a substance is the amount of time it takes for a decreasing exponential function to decay.

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