ELF.01.8 – Solving Word ELF.01.8 – Solving Word Problems Using LogarithmsProblems Using Logarithms

MCB4U - SantowskiMCB4U - Santowski

(A) Examples(A) Examples The logarithmic function has applications for solving The logarithmic function has applications for solving

everyday situations:everyday situations:

ex 1. Mr. S. drinks a cup of coffee at 9:45 am and his 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 coffee contains 150 mg of caffeine. Since the half-life of caffeine for an average adult is 5.5 hours, determine how caffeine for an average adult is 5.5 hours, determine how much caffeine is in Mr. S.'s body at class-time (1:10pm). much caffeine is in Mr. S.'s body at class-time (1:10pm). Then determine how much time passes before I have 30 Then determine how much time passes before I have 30 mg of caffeine in my body.mg of caffeine in my body.

ex 2. The value of the Canadian dollar , at a time of ex 2. The value of the Canadian dollar , at a time of inflation, decreases by 10% each year. What is the half-inflation, decreases by 10% each year. What is the half-life of the Canadian dollar?life of the Canadian dollar?

(A) Examples(A) Examples

ex 3. The half-life of radium-226 is 1620 a. ex 3. The half-life of radium-226 is 1620 a. Starting with a sample of 120 mg, after Starting with a sample of 120 mg, after how many years is only 40 mg left? how many years is only 40 mg left?

ex 4. Find the length of time required for ex 4. Find the length of time required for an investment of $1000 to grow to $4,500 an investment of $1000 to grow to $4,500 at a rate of 9% p.a. compounded quarterly. at a rate of 9% p.a. compounded quarterly.

(A) Examples(A) Examples ex 5. Dry cleaners use a cleaning fluid that is purified by ex 5. Dry cleaners use a cleaning fluid that is purified by

evaporation and condensation after each cleaning cycle. evaporation and condensation after each cleaning cycle. Every time it is purified, 2% of the fluid is lostEvery time it is purified, 2% of the fluid is lost

(a) An equipment manufacturer claims that after 20 (a) An equipment manufacturer claims that after 20 cycles, about two-thirds of the fluid remains. Verify or cycles, about two-thirds of the fluid remains. Verify or reject this claim.reject this claim.

(b) If the fluid has to be "topped up" when half the (b) If the fluid has to be "topped up" when half the original amount remains, after how many cycles should original amount remains, after how many cycles should the fluid be topped up?the fluid be topped up?

(c) A manufacturer has developed a new process such (c) A manufacturer has developed a new process such that two-thirds of the cleaning fluid remains after 40 that two-thirds of the cleaning fluid remains after 40 cycles. What percentage of fluid is lost after each cycle?cycles. What percentage of fluid is lost after each cycle?

(B) Examples with Data Analysis(B) Examples with Data Analysis

Given the following data of numbers of bacteria:Given the following data of numbers of bacteria:

(i) use graphing technology to graph the data(i) use graphing technology to graph the data (ii) use graphing technology to determine a reasonable (ii) use graphing technology to determine a reasonable

regression equation for an algebraic model of the dataregression equation for an algebraic model of the data (iii) using your equation, how many bacteria would you (iii) using your equation, how many bacteria would you

expect in 9 days?expect in 9 days? (iv) what is the doubling period of the bacteria?(iv) what is the doubling period of the bacteria? (v) how long does it take to get 2000 bacteria?(v) how long does it take to get 2000 bacteria?

DayDay 00 11 22 33 44

# of bacteria# of bacteria 300300 378378 476476 600600 756756

(B) Homework(B) Homework

Nelson Text, p132, Q11-16Nelson Text, p132, Q11-16 Nelson Text, p153, Q4-8,11,12Nelson Text, p153, Q4-8,11,12 Photocopy page 100-101 from Houghton Photocopy page 100-101 from Houghton

Math 12Math 12