4.3 Use Functions Involving e PROJECT DUE: Tomorrow Quiz: Tomorrow Performance Exam: Friday *We will be having a book check tomorrow…. BRING BOTH BOOKS TOMORROW!

Vocabulary The number denoted by the letter e is called the natural base e or the Euler number. –Think of e like you do π –e is approximately A function of the form f(x) = ae rx is called a natural base exponential function.

Natural base exponential function f(x) = ae rx –If a is positive and r is positive OR if a is negative and r is negative: GROWTH –If a is positive and r is negative OR a is negative and r is positive: DECAY

Example 1: Simplify the expression a) e 6 e 4 = b) c) (-2e x ) 3 =

Example 2: Graph the function. State the domain and range. a) y = 4e -x + 5

Example 2 cont’d: Graph the function. State the domain and range. b) y = e 2(x+1) - 2

Example 3: A population of bacteria can be modeled by the function P = 70e 0.22t where t is the time (in hours). Estimate the population after 4 hours.

Vocabulary Continuously Compounded Interest –When interest is compounded continuously, the amount A in an account after t years is given by the formula A = Pe rt. P is the principal r is the annual interest rate expressed as a decimal.

Example 4: You deposit $500 in an account that pays 3% annual interest compounded continuously. What is the balance after 2 years? A = Pe rt

Homework P. 142 #1-28 (Green book) Finish Project – to Study for Quiz, and Performance Exam BOOK CHECK TOMORROW!