10.5 Base e and Natural Logarithms Students will be able to… 1) Evaluate expressions involving the natural base and natural logarithms. 2) Solve exponential equations using natural logarithms.

N A yearly quarterly monthly weekly daily hourly Compound Interest Investigation

 An exponential function with base e is called a natural base exponential function.  The natural logarithm is sometimes denoted ln e x but more often abbreviated or lnx.  It is the inverse of the natural base exponential function y=e x  log e x = lnx Base e and Natural Logarithms

Consider the graph of y = e x

Write an equivalent exponential or logarithmic equation. a) b) Example 1

 Since the natural base function and the natural logarithm function are inverses, these two functions can be used to “undo” each other. Inverse Property

 Evaluate each expression: a)b) Example 2

Solve: a)b) Equations with e and ln

Suppose you deposit $1000 in an account paying 5% annual interest compounded continuously. ( A = Pe rt ) a)What is the balance after 10 years? b)How long will it take for the balance in your account to reach at least $1500? Application : Interest compounded Continuously

 Text p. 557 #s 8-11, 13, 14, 16, 17 Partner Practice

 Text p #s 28  Equations only from #s 38 – 51  #s all Homework