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Understanding Logarithmic Functions and Their Applications in Real-Life Scenarios

This guide reviews key concepts related to logarithmic functions, including properties, change of base, and solving for variables. It addresses practical applications such as Newton's Law of Cooling, population growth, and compound interest, guiding students through problem-solving strategies. Following the review worksheet, students are encouraged to work individually on problems, checking their answers and utilizing resources for any challenges faced. Suggested review problems are also provided to reinforce understanding of the material.

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Understanding Logarithmic Functions and Their Applications in Real-Life Scenarios

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  1. Homework Check • Court Case: C = 22, k = -.007753359 • Prosecutors – Interpreting the last bullet as feeling totally better with a temp. of 98.6, then time of death would be 3:13, which is after Steve’s alibi. • Defenders – Interpreting the last bullet as still feeling sick, with a temp. of anything higher than 99.3, then time of death would be before 3:10 while Steve had an alibi. • 53.382 min total or 42.382 min after the temp was 275. • 379.236 • 3:49 am

  2. Review • Properties of Logs: • ln 1 and log 1 = 0 • lne = 1 • logbb = 1 • elnx = x • blogbx = x • Change of Base:

  3. Review Rules for Expanding & Condensing Product Rule: Quotient Rule: Power Rule: • How to solve for x: • Getting single log and solve. • Getting e alone and solve. • Circle method or log/ln or e both sides.

  4. Review • Applications (graphically & algebraically) • Population A(n) = P0(1 ± r)n • Half & Double Life A(n) = P0(1/2)n/hl A(n) = P0(2)n/dl • Compound interest A(t) = P0(1 + r/n)nt • Compound continuously A(t) = Pert • Newton’s Law of Cooling T = Cekt + R

  5. Review • 4 Stations are set up with the answers to the review worksheet. • Working individually, work out the problems in any order, then check your answers as you go. • If you get stuck, look in your notes or borrow a book to try to find the answer. • Still no luck? Go take a look (without your pencil) at the answer to figure it out. • When finished look at the suggested review problems in the book and make sure you understand the material from the quizzes. • pg 345 #19, 21, 27-33 odd, 43 – 49 odd, 53 – 57 odd, 63, 65, 69, 75 – 79 odd and 95

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