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Take-Home Quiz and Log Equations Review Instructions

This document outlines the details for the upcoming take-home quiz due Wednesday. We’ll review the quiz during lunch, right after our class. If you have lost Worksheet #1c, it is available on the website. Make sure to complete necessary problems from the workbook and worksheets, and remember that showing your work is essential to receive credit. Additionally, we've covered various examples involving log equations, exponential growth and decay, with several examples provided for practice.

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Take-Home Quiz and Log Equations Review Instructions

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  1. NEWS • Still pondering what to do with the test • Quiz will be a TAKE-HOME (due Wednesday) • Wednesday at lunch I will be going over the test (we have class right before) Free Powerpoint Templates

  2. TAKE HOME QUIZ • Worksheet #1c  ON WEBSITE if you lost it • Worksheet #3 • Workbook p.159 #2e • Workbook p.160 #3d (SHOW YOUR WORK OR YOU GET ZERO!!) • Workbook p.174 #3b • Workbook p.176 #7e • Workbook p. 176 #8f • Workbook p. 177 #12b • Workbook p.177 #14c • Workbook p.179 #25b

  3. Let’s go over a log question… p. 177 #12a 4ln2x + ln(6/x) – 2ln2x = ln(2x)4 + ln(6/x) – ln(2x)2 = ln16x4 + ln(6/x) – ln4x2 = ln(16x4∙6) x∙4x2 = ln(96x4) 4x3 = ln24x

  4. Solving Log Equations Example 1 log(x+1) = 1 – log(x-2) Restrictions: x>-1 and x>2 log(x+1) + log(x-2) = 1 log((x+1)(x-2)) = 1(addition law) 101 = (x+1)(x-2)(change to exponential form)

  5. Solving Log Equations Example 1 x2 – x – 2 = 10 x2 – x – 12 = 0 (x+3)(x-4) = 0(factoring) x=-3 and x=4 Because of the restrictions, we reject x=-3 S={4}

  6. Solving Log Equations Example 2 ln(x+2) = ln(-x+6) + ln(x-1) Restrictions: x>-2, x<6, x>1 ln(x+2) = ln((-x+6)(x-1)) (x+2) = (-x+6)(x-1)(divide both sides by ln) x+2 = -x2 + 7x - 6(expand) -x >-6 x<6

  7. Solving Log Equations Example 2 x2 – 6x + 8 = 0 (x-2)(x-4) = 0(factoring) x=2 and x=4 Both fit the restrictions S={2,4}

  8. Growth & Decay Intro to Exponential Functions

  9. Formulas GROWTH = (P)(1+interest rate)time DECAY = (P)(1-interest rate)time

  10. Example 3 How much money will you have if you invest 700$ at 7.5% compounded annually for 15 years? f(x) = (700)(1.075)15 = $2071.21

  11. Example 4 You buy a car for $25000. If it depreciates by 4.3% annually, what’s the value of the car 10 years later? f(x) = (25000)(1- 0.043)10 f(x) = (25000)(0.957)10 = $16108.66

  12. Example 5 An investment of $600 at 8% grows to $7280. For how long was it invested? 7280 = (600)(1.08)x 12.13 =(1.08)x log1.0812.13 = x(change to log form) x = (log12.13)/(log1.08) = 32.43

  13. Example 6 An investment at 6% grows to $1296 in 12 years. What was the initial investment? 1296 = (P)(1.06)12 1296 =(P)(2.012) $644.07 = P

  14. Example 7 An investment of $900 grows to $1340 in 8 years. What rate of interest did the investment earn? 1340 = (900)(1+r)8 1.48 =(1+r)8 (1.48)1/8 =(1+r)8∙(1/8)(to get rid of the exponent)

  15. Example 7 An investment of $900 grows to $1340 in 8 years. What rate of interest did the investment earn? 1.051 = 1+r 0.051 = r So 5.1%

  16. HOMEWORK • TAKE HOME QUIZ • Workbook p.137 #3,4,5,6 p.180-181 #27, 28 • Worksheet Side 2 #1,2

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