Calculus Ia MATH 1125
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This 3 page Class Notes was uploaded by Mary Veum on Thursday September 17, 2015. The Class Notes belongs to MATH 1125 at University of Connecticut taught by John Haga in Fall. Since its upload, it has received 17 views. For similar materials see /class/205824/math-1125-university-of-connecticut in Mathematics (M) at University of Connecticut.
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Date Created: 09/17/15
Section 15 Section 15 Exponential Functions An exponential function can be written in the form y f 96 am where a is a positive constant What does this mean Consider the following cases 0 z n Where n is a positive integer 00 o z in Where n is a positive integer o z E Where p and q are integers q gt 0 this is a rational number 1 o z is an irrational number ie not rational Examples of real life phenomena which have exponential functions as models Section 15 2 Graphs of Exponential Functions oagt1 00ltalt1 Example 1 Graph the following exponential function using transformations and state the domain and range we 2 7 4r Section 15 Laws of Exponents If a and b are positive numbers and z and y are any real numbers7 1 aHy away 2 am L ay am y e e W NonLaws of Exponents 1 aHy 31 1m ay 2 abm 31 ab 3 a by 31 1m bm So f 2 7 4 m 2 7 and g 2m 2w2 2 2 but h 32m 31 6w Example 2 Simplify the following expression so that it is written as a constant times a power of x SSz 2z Example 3 Solve the equation 2 16w 8 1 for x The Numb er 6 De nition The number 6 has a variety of de nitions depending on which point of View you7d like to take and what knowledge is assumed For now we de ne e to be the constant so that the exponential function fx em has a tangent line with slope 1 at the point 01 It turns out that e 271828 Example 4 Starting with the graph of y 6 nd the equation of the graph that results from re ecting about the line z 72
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