Exponentials and Order of Operations

I.  Quiz

II.  Homework

III.  Definition of an Exponential

Examples:  3² = (3)(3),  4³ = (4)(4)(4)

Definition:  xⁿ = (x)(x)(x)(x)(x)...(x) where there are n x's.

Exercises:   Evaluate

A)  2³  

B)  3⁴

 IV.  Order of Operation

We read the following symbols in order:

1)  () and ||

2)  Exponents

3)  X and /

4)  + and -

5)  If there is a tie we read from left to right.

Exercises:

A)  (5 + 2² x 3 )/ 7

B)  7  + (3 + 2)/3

C)  |3- 6|²/-3

D)  (-1/2 + 1/3)(6)

E)  -1/2 + 1/3x6

F) [2/5 - 1/3]/[1/3 - 1/5]

V.   Evaluating Algebraic Expressions

 Example:

Consider  x² + 3xy + 2x

What do we get if x = 1 and y = -2?

Solution:

(1)² + 3(1)(-2) + 2(1) = 1 - 6 + 2 = -5 + 2= -3

Exercises:

Evaluate  |2x - y|/|x² - y²|

A)  When x = 1, y = 2

B)  When x = 3, y = 6

C)  When x = 2, y = 2

VI.  Applications

Beginning at an elevation of 6,500 feet, you take a chair that ascends at a rate of 100 ft/min for 8 minutes.  Then you ski down a run descending at a rate of 200 ft/min for three minutes and take a different chair lift that ascends at a rate of 50 ft/minute for 5 minutes.  What is you elevation now?