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NEWS

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. TAKE HOME QUIZ. Worksheet #1c  ON WEBSITE if you lost it Worksheet #3

jacob-potts
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NEWS

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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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