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ELF.01.8 – Solving Word Problems Using Logarithms

ELF.01.8 – Solving Word Problems Using Logarithms. MCB4U - Santowski. (A) Examples. The logarithmic function has applications for solving everyday situations:

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ELF.01.8 – Solving Word Problems Using Logarithms

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

  2. (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?

  3. (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.

  4. (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?

  5. (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?

  6. (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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