Transcript xy = 2 x - Souderton Math

6.2 Exponential Functions
Objective: Classify an exponential function
as representing exponential growth or
exponential decay.
Calculate the growth of investments under
various conditions.
Standard: 2.11.11.C
Graph and interpret rates of decay/growth
In an exponential function, the base is fixed
and the exponent is the variable.
The function f(x) = bx is an exponential
function with base b, where b is a positive
real number other than 1 and x is any real
number.
Examine the graph of y= 2x.
Notice that as the x-values decrease,
the y-values get closer and closer to
0, approaching the x-axis as an
asymptote.
An asymptote
is
a
line
that
xa graph
y =approaches
2x
The graph of
-3 =1/8
x
-3
2
y
=
2
(but does
not
reach)
as
-2 = ¼
-2
2
its x- or -1y-valuesapproaches
become the
x axis – but
-1
2
=
½
very large
or
very
small.
never
reaches it!
0
20 = 1
1
21 = 2
√2
2 √2 =2.67
2
22 = 4
3
23= 8
Notice the domain
of y= 2x includes
irrational numbers,
such as √2
y= 2x
The graph of f(x) = 2x and g(x) = (1/2)x
exhibit the two typical behaviors for
exponential functions.
g(x) =
g(x) = (1/2)x is a
decreasing
function because
its base number is
a positive number
less than one
(1/2)x
f(x) = 2x
f(x) = 2x is an
increasing
exponential
function
because its
base is a
positive
number greater
than one
More Examples:
Graph f(x) = 2x and give the y-intercept.
• Y = ¼ * f(-x)
• Y = 1/3* f(x)
Ex. 2
Principal = $100
Annual Interest = 5 %
Time (t) = 10
Effective Yield:
Application Investments
• Suppose that you buy an item for $100
and sell the item one year later for $105.
In this case, the effective yield of your
investments is 5%. The effective yield is
the annually compounded interest rate that
yields the final amount of an investment.
You can determine the effective yield by
fitting an exponential regression equation
to two points.
* Ex 3A.
A collector buys a painting for $100,000 at the beginning of
1995 and sells it for $150,000 at the beginning of 2000. Use
an exponential regression equation to find the effective yield.
Ex 3B.
Find the effective yield for a painting bought for $100,000 at
the end of 1994 and sold for $200,000 at the end of 2004.
Homework
Pg. 367-368 #10-36 even