8.2 Properties of Exponential Functions 8.3 Logarithmic Functions as Inverses

List Sequence of Transformations Transformations of

Ex4) Since a 200-mg supply of technetium-99m has a half- life of 6 hours, find the amount of technetium-99m that remains from a 50-mg supply after 25 hours. Half-Life

e and the Pe rt Formula Continuously Compounded Interest: time in years amount in initial rate of account amount interest

e and the Pe rt Formula Ex5) Suppose you invest $100 at an annual interest rate of 4.8% compounded continuously. How much will you have in the account after 3 years? Ex6) Suppose you invest $1300 at an annual interest rate of 4.3% compounded continuously. Find the amount you will have in the account after 5.5 years.

Intro to Logarithms A logarithmic function tells us what exponent was used get an answer for a base to an exponent. Exponential function: The input is the EXPONENT A logarithmic function tells us what exponent was used get an answer for a base to an exponent. The logarithm to the base b of a positive number y is defined: A logarithmic function is the inverse of an exponential function, so: An exponential function tells us what answer we get when we take a base to an exponent. ***Inverses do the opposite of each other… The output is the EXPONENT

Intro to Logarithms Ex 1) Write each equation in logarithmic form: Ex 2) Write each equation in exponential form: Common Logarithm: a logarithm with base 10

Evaluating Logarithms

Ex 4) Evaluate:

Graphing Logarithms The inverse of this exponential function is its reflection over the line y = x Characteristics?

HW:8.2 # all 8.3 # 6-24 even, odd 8.2 Properties of Exponential Functions 8.3 Logarithmic Functions as Inverses