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Pre-Calc Lesson 5-2

Pre-Calc Lesson 5-2 Growth and Decay: Rational Exponents Rational Exponents: ( Fractions as exponents) b 1/q = q b 1 so b p/q = q b p Simplify:

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Pre-Calc Lesson 5-2

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  1. Pre-Calc Lesson 5-2 • Growth and Decay: Rational Exponents • Rational Exponents: (Fractions as exponents) • b1/q =q b1 • so bp/q = q bp • Simplify: • 161/4 2. 16-1/4 3. 82/3 4. 8-2/3 • 5. Suppose a car presently worth $8200 depreciates 20% • per year. About how much will it be worth 2 years and • 3 months from now?

  2. 1st---3 months is what part of a year---? ¼ So 2 years and 3 months = 2 ¼ or 9/4 years. (Or 2.25) Therefore this is an exponential decay problem so: C(t) = A0(1 - r)t C(2.25) = 8200(1-0.20)2.25 = 8200(.80)2.25 = 4963 or $4963 6. Solve: 2x = 1 8 2x = 1 23 2x = 2-3 so x = - 3

  3. 9x+1 = 27 • (32)x+1 = (3)3 • (3)2x+2 = ((3)3))1/2 • (3)2x+2 = (3)3/2 • 2x+2 = 3/2 • 2x = 3/2 - 2 • 2x = - ½ • x = - ¼ • 4x3/2 = 32 • x3/2 = 8 • (x3/2)2/3 = (8)2/3 • x = 3 82 • x = 3 64 • x = 4

  4. Solve: 9. (x – 1)-1/4 - 2 = 0 (x – 1)-1/4 = 2 ((x – 1)-1/4)-4 = (2)-4 (x – 1) = 1 16 x = 1 + 1 or 17 16 16 Example: 10. A house bought 5 years ago for $100,000 was just sold for $135,000. to the nearest tenth of a percent what was the annual growth rate. Use A(t) = A0(1 + r)t

  5. so  135,000 = 100,000(1 + r)5 1.35 = (1+r)5 (1.35)1/5 = ((1+r)5)1/5 1.061859 = 1 + r .061859 = r or .062 or 6.2% = r

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