Transcript 4.3 Use Functions Involving e

4.3
Use Functions Involving e
PROJECT DUE: Tomorrow
4.1-4.2 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 2.718281828.
• A function of the form f(x) = aerx is called a
natural base exponential function.
Natural base exponential function
•f(x) =
rx
ae
– 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) e6 • e4 =
b) 21e
7e
8
2
c) (-2ex)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 = e2(x+1) - 2
Example 3:
• A population of bacteria can be modeled
by the function P = 70e0.22t 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 = Pert.
• 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?
Homework
• P. 142 #1-28 (Green book)
• Finish Project
– Email to
[email protected]
• Study for 4.1-4.2 Quiz, and Performance
Exam
BOOK CHECK TOMORROW!