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: 1.16 1/4.

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Presentation transcript:

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: / / / /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?

1 st ---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) = A 0 (1 - r) t C(2.25) = 8200(1-0.20) 2.25 = 8200(.80) 2.25 = 4963 or $ Solve: 2 x = x = x = 2 -3 so x = - 3

7.9 x+1 = 27 (3 2 ) x+1 = (3) 3 (3) 2x+2 = ((3) 3) ) 1/2 (3) 2x+2 = (3) 3/2 2x+2 = 3/2 2x = 3/ x = - ½ x = - ¼ 8.4x 3/2 = 32 x 3/2 = 8 (x 3/2 ) 2/3 = (8) 2/3 x = x = 3 64 x = 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 = or 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) = A 0 (1 + r) t

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