10.1 Exponential and Logarithmic Relations

Algebra II w/ trig

Exponential Functions – has the form y= abx, where a ≠0, b>0, and b≠1

- y represents the quantity after time is expired

- a represents the initial quantity and the y intercept

- b represents the base- x represents the time

I. 2 types of exponential functions

Exponential Growth: if a>o and b>1Exponential Decay: if a>o and 0< b <1

A. Exponential Growth or Decay?1. y = 0.3(1.2)x 3. y = 3(0.6) x

2. y = -5 (4/5)x 4. y = 5(4)-x

B. Sketch the graph and state the domain and the range.Parent equation: y = abx With shifts y = abx-h + k

To graph: 1. Sketch y= abx, use a table with x values 0 and 1

2. Then move your 2 points h units left or right, and k units up or down

3. Then sketch the graph with the 2 new points

a. f(x) = (½)x b. f(x) = 3 x

c. f(x)= 3●2x-1 – 4 d. f(x) = 2 ●3x-2 + 1

II. Exponential Equations/ InequalitiesA. Properties of Rational Exponents

a. am ●an = am+n

b. (am)n = amn

c. am ÷ an = am-n

B. Simplify each expression.d. (3√2) √2 e. (x √6)(x √5)

e. (m √28) √7 f. 2x π (5x3π )

f. (c √6) √63 g. 25 √2 ● 125 √2

g. (x √6 y 3√2) √2

C. Property of Equality for Exponential FunctionsIf b is a positive number other than 1,

then bx = by , if and only if x = y

D. Property of inequality of Exponential FunctionsIf b > 1, then bx > by , if and only if x > y , and

bx < by , if and only if x< y

E. Solve each equation or inequality. Check your solutions.

a. 2x+1 = 22x + 3 b. 32x-1= 3x+2

c. 4x+1 = 82x+3 d. 23x = 4x+2

e. 32x-1 = 1/9 f. gx-2= 1/16

g. 4√x= 16√5 h. 3x-4<1/27

i. 42x-2>2x+1 j. 52x<125x-5