UNIT 3: EXPONENTS, RADICALS, AND EXPONENTIAL EQUATIONS Final Exam Review.

Upload
angelicaallison 
Category
Documents

view
247 
download
0
description
Transcript of UNIT 3: EXPONENTS, RADICALS, AND EXPONENTIAL EQUATIONS Final Exam Review.
UNIT 3: EXPONENTS, RADICALS, AND
EXPONENTIAL EQUATIONS
Final Exam Review
TOPICS TO COVERExponent RulesConverting Radicals to Fractional ExponentsConverting Fractional Exponents to RadicalsExponential Growth and DecayWord Problems
EXPONENT RULESMathematical Expressions can be simplified used exponent rulesHere are all of the rules:ADDING AND SUBTRACTING EXPRESSIONSMULTIPLYING EXPRESSIONSRAISING A POWER TO A POWERDIVIDING EXPRESSIONSNEGATIVE EXPONENTSZERO EXPONENTS
ADDING AND SUBTRACTING EXPRESSIONSWhen you are adding and subtracting exponents, you must:COMBINE LIKE TERMS only!Make sure to DISTRIBUTE the NEGATIVE when subtracting
Example:(4x2 + 9x – 6) + (7x2 – 2x – 1) = 11x2 + 7x – 7
(3x2 + 5x – 8) – (5x2 – 4x + 6) = 2x2 + 9x – 14
MULTIPLYING EXPRESSIONSWhen you are multiplying expressionsMULTIPLY the whole numbersADD the exponents
Example:(4x3)(2x2) = 8x5
(4x5)(3x2) = 12x7
RAISING A POWER TO A POWERWhen you are raising a power to a power:RAISE the whole numbers to the powerMULTIPLY the exponents
Example:(5x2)4 = 625x8
(3x6)3 = 27x18
DIVIDING EXPRESSIONSWhen you are dividing expressions:DIVIDE the whole numbersSUBTRACT the exponents
Example: =
=
NEGATIVE EXPONENTSWhen you have a negative exponentMOVE the negative exponent “TO THE OTHER BUNK”, meaning, move it to the other side of the FRACTION
When you move it, change the exponent to a POSITIVE because not it’s “HAPPY”
Example: =
= =
ZERO EXPONENTSWhen you have a zero exponentThe answer is always ZERO
Example: (5x4y2)0 = 1
= 1
PRACTICE ALL EXPONENT RULES1. (5x2 – 5x + 2) + (6x2 + 2x – 10) 2. (3x2 + 6x – 4) – (6x2 – 2x + 9)3. (6x4)(5x2)4. (4x2)3
5. (3x2y)0
CONVERTING A RADICAL INTO A FRACTIONAL EXPONENTParts of a radicalWhen converting a radical to a fractional exponent:The power inside the radical becomes the NUMERATORThe number in the INDEX becomes the DENOMINATOR
Example:
CONVERTING A RADICAL INTO A FRACTIONAL EXPONENTNow try these:
CONVERTING A FRACTIONAL EXPONENT INTO A RADICALWhen converting a fractional exponent into a radical:The numerator becomes the power INSIDE the radical
The denominator becomes the number in the INDEX
Example:
CONVERTING A FRACTIONAL EXPONENT INTO A RADICALNow try these:
EXPONENTIAL GROWTH AND DECAYExponential Functions can either represent GROWTH or DECAYEvery function follows this formula:y = a bx
a is the INITIAL valueb is the GROWTH or DECAY rateIf the problem is growth, use (1 + rate) for bIf the problem is decay, use (1 – rate) for b
x is the TIME
EXPONENTIAL GROWTH AND DECAYExampleWrite the equation for this situation:The amount of movies made in 2015 was 1,255. The number is expected to increase by 2.1% every year.
Answer: y = 1255(1 + 0.021)x
EXPONENTIAL GROWTH AND DECAYNow thy theseWrite an equation for these situations:1. The population of an ant colony with 5,056
members increases by 5.6% every year.2. The number of people who live in North
Dakota (who currently has 739,482 people) decreases every year by 1.3%.
WORD PROBLEMSThere are many real life situations that use exponential growth and decay. You can use these equations in order to predict outcomes in the future.In order to do this, use your calculator to put in the equation and use the table to find values.
WORD PROBLEMSTry this one:
The model y = 604000(1 + 0.045)x represent the population of Washington DC after 1990.1. Find the initial population2. Is this a growth or decay problem?3. Predict the population in 1995.4. In what year will the population reach 1,000,000?
ALL DONE