Transcript Chapter 5 Lesson 2 - Elgin Local Schools

Pre-Calc
Lesson 5-2
Growth and Decay: Rational Exponents
Rational Exponents: (Fractions as exponents)
b1/q =
q
b1
so bp/q =
Simplify:
1. 161/4
2. 16-1/4
q
bp
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
8. 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