MAT170StudyGuide_Caldwell.pdf MAT 170
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This 2 page Study Guide was uploaded by Abby Romero on Tuesday March 24, 2015. The Study Guide belongs to MAT 170 at Arizona State University taught by Wendy Caldwell in Spring2015. Since its upload, it has received 123 views. For similar materials see Precalculus in Liberal Arts at Arizona State University.
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Date Created: 03/24/15
MAT 170 Midterm 2 Final Exam Material Rules of Exponents x2x1o x21o 2 x12 x2x1o x21o 2 x20 0 x0 1 0 Anything to the 0 power is 1 3 x x Example 0 2x23 3x2 23x6 32x2 8x6 9x2 72x26 72x8 0 Distribute the exponent and work step by step Rules of Logarithms 10gbx 10gby 10gbx 39y x 10819 x 10819 y 10819 5 1013190716 C 10gbm Change of Base logb a loga logb gt YOU CANNOT TAKE THE LOG OF A NEGATIVE NUMBER Logarithmic Form into Exponential Form y bquot gt 10gby x Concavity Intervals Concave Up Concave Down k Exponential Growth Decay Formula ya bx Where ainitial population bgrowth decay factor and xunit of time 0 Growth b gt 1 Decay 0 lt b lt1 0 If b is less than 1 it is decaying if it is greater than one it is growing rPercent Change r New ValuePrevious Value Previous Value How to find the decay factor if the problem only gives you the initial value and whatever amount is left Amount Leftover Initial Value Example In 2004 there are 218 alpacas 8 years later there are 187 So divide 187 by 218 to get the decay factor of about 0868 How to find growth decay factor from a table Divide the new value by the previous value New Value Previous Value How to find the growth factor of x day Take growth decay factor and raise it to x power If finding the 12hour growth factor raise it to the 5 power 12 hours is 5 of a 24hour day To reverse this and find the 1unit growth factor decay factor and raise root it with that number for example if given the 5 day growth factor to find the 1 day growth factor take the W of that number 0 How to calculate Percent Change b 1r New Value Previous Value x 100 Previous Value Finding Roots Graphs 0 Set equal to zero and solve 0 Ex Given xS set it equal to zero and your root would be 5 o If given an unfactorable polynomial plug the number into the quadratic and solve 0 IF A NEGATIVE NUMBER APPEARS UNDER THE SQUARE ROOT DO NOT PROCEED THE ANSWER IS NO SOLUTION o NUMBERS WITH A DENOMINATOR OF 0 ARE UNSOLVABLE THE ANSWER IS NO SOLUTION 0 Finding X amp Y Coordinates with the Quadratic Formula 0 XCoordinate of the Vertex can be find by using g o YCoordinate of the Vertex is whatever ycoordinate exists after solving the equation above 0 Odd Degree polynomials have opposite end behavior even degree polynomials have the same end behavior
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