Math_41_Exam_3_review

Math_41_Exam_3_review - Math 41 Review for Exam 3 3.1...

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Math 41 Review for Exam 3 3.1 Exponential Functions - An exponential function has the form ( ) x f x a = , where a>0 and a≠1. You need to be able to evaluate exponential functions on your calculator. You need to be able to graph exponential functions by hand. All exponential functions of the form ( ) x f x a = have a horizontal asymptote at y=0 . You need to be able to do a transformation of an exponential function. An important exponential function is ( ) x f x e = . You need to be able to evaluate the natural exponential function on your calculator and by hand (when possible). One of the most useful applications of the exponential function is interest. You need to know the formulas for interest: 1) For n compoundings per year, (1 ) nt r n A P = + , where A is the future amount, P is the principal, r is the annual interest rate (in decimal form), and t is the time in years, 2) For continuous compounding, rt A Pe = . 3.2 Logarithmic Functions - Remember that a logarithmic function is the inverse function of the exponential function. For x>0, a>0 and a≠1, log y a y x iff x a = = . Remember that a logarithm is an exponent ! You need to be able to evaluate logs by hand, and on your calculator. Remember that the log button on your calculator only evaluates common logs (base 10). You need to be able to graph a log function by hand. You can do this by graphing it inverse exponential function, switching the inputs and outputs of the exponential function, and plotting the new points for the log function. One of the most useful log functions is the natural log function (ln x ). This is just the inverse of the natural exponential function. You need to be able to evaluate natural logs by hand and with your calculator. Remember that the base of the natural log function is e , even though it is not explicitly written. Properties of Exponents : 1. x y x y a a a + = 2. x x y y a a a - = 3. 1 x x a a - = 4. 0 1 a = 5. ( ) x x x ab a b = 6. ( ) x y xy a a = 7. ( 29 x x x a a b b = 3.3 Properties of Logarithms - You need to be able to convert an exponential expression to a logarithmic expression, and vice versa. You need to know the 3 change of base formulas: 10 10 log log ln log log log ln b a b x x x x a a a = = = . Remember that your calculator can only evaluate logarithms base 10 (common log) or base e (natural log). You need to know the
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following properties of logarithms in order to expand or condense log expressions: log( ) log log ln( ) ln ln log( ) log log ln( ) ln
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Math_41_Exam_3_review - Math 41 Review for Exam 3 3.1...

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