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?

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

7. 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

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

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