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Exponential Functionsand the number e
Precalculus11-2 and 11-3
p. 704
CalculatorGraph y = bx
b = 0.5b = 0.75
b = 2b = 5
Characteristics of graphs of y = bx
b > 1 0 < b < 1
Domain all real numbers all real numbers
Range
y-inercept
Behavior
Horizontal asymptote
Vertical asymptote
Characteristics of graphs of y = bx
b > 1 0 < b < 1
Domain all real numbers all real numbers
Range {y | y > 0} {y | y > 0}
y-inercept
Behavior
Horizontal asymptote
Vertical asymptote
Characteristics of graphs of y = bx
b > 1 0 < b < 1
Domain all real numbers all real numbers
Range {y | y > 0} {y | y > 0}
y-inercept (0, 1) (0, 1)
Behavior
Horizontal asymptote
Vertical asymptote
Characteristics of graphs of y = bx
b > 1 0 < b < 1
Domain all real numbers all real numbers
Range {y | y > 0} {y | y > 0}
y-inercept (0, 1) (0, 1)
Behavior Continuousone-to-oneincreasing
Continuousone-to-onedecreasing
Horizontal asymptote
Vertical asymptote
Characteristics of graphs of y = bx
b > 1 0 < b < 1
Domain all real numbers all real numbers
Range {y | y > 0} {y | y > 0}
y-inercept (0, 1) (0, 1)
Behavior Continuousone-to-oneincreasing
Continuousone-to-onedecreasing
Horizontal asymptote
negative x-axis positive x-axis
Vertical asymptote
Characteristics of graphs of y = bx
b > 1 0 < b < 1
Domain all real numbers all real numbers
Range {y | y > 0} {y | y > 0}
y-inercept (0, 1) (0, 1)
Behavior • Continuous• one-to-one• increasing
• Continuous• one-to-one• decreasing
Horizontal asymptote
negative x-axis positive x-axis
Vertical asymptote none none
CalculatorGraphy = 4x
y = 4x + 2y = 4x – 3
CompareO All the graphs are continuous, increasing,
and one-to-one.
CompareO All the graphs are continuous, increasing,
and one-to-one.O The y-intercept and horizontal asymptotes
for each graph are different.
CompareO All the graphs are continuous, increasing,
and one-to-one.O The y-intercept and horizontal asymptotes
for each graph are different.O Only one graph has an x-intercept
Exponential Growth or Decay
N is the final amount
Exponential Growth or Decay
N is the final amount
Exponential Growth or Decay
N0 is the initial amount
N is the final amount
Exponential Growth or Decay
N0 is the initial amount
r is the rate of growth or decay per time period
N is the final amount
Exponential Growth or Decay
N0 is the initial amount
r is the rate of growth or decay per time period
t is the number of time periods
Compound Interest
A is the final amount
Compound Interest
A is the final amount
Compound Interest
P is the principal or initial investment
A is the final amount
Compound Interest
P is the principal or initial investment
r is the annual interest rate
A is the final amount
Compound Interest
P is the principal or initial investment
r is the annual interest rate
n is the number of times interest is paid
A is the final amount
Compound Interest
P is the principal or initial investment
r is the annual interest rate
t is the number of years
n is the number of times interest is paid
The Number e
The Number eO e is not a variable.
The Number eO e is not a variable.O e is a constant like .π
The Number eO e is not a variable.O e is a constant like .π
The Number eO e is not a variable.O e is a constant like .π
