WoooooooooRRRRRRDDDDD!!!! (Vocab)
An exponential function is a function with the general form y = ab^x, where x is a real number, a ≠ 0,
b > 0, andb ≠ 1.
You can use an exponential function to model growth when b > 1. When b > 1, b is the growth factor.
An asymptote is a line that a graph approaches as x or y increases in absolute value.
An exponential function can be used to model decay when 0 < b < 1. When b < 1, b is a decay factor.
List of Good and Bad things about Exponential Equations
BAD -- VERY BAD!!!! |
VERY NICE!!!! GOOD!!! |
Exponential Growth -- when the base is one or greater
Exponential Decay -- When the base is less than one
Exponential Decay -- When the base is less than one
Example Problems #1
Practice Problems #1
Growth Factor -- 1 + r
(Where r is the percent increase of growth rate)
Equation to use is:
y=ab^x
x -- Number of years after 2000
y -- population in millions
(Where r is the percent increase of growth rate)
Equation to use is:
y=ab^x
x -- Number of years after 2000
y -- population in millions
Population Problem
Horizontal Asymptote -- Where a graph approaches a line but never crosses it (Horizontal will be side to side)
Example Problems #2
Practice Problems #2
Warning: Toughest problem in this section!