Feb 25­3:17 PM

Activity:  Investigating Graphs of Exponential Functions, pg. 465

An Exponential Function involves  the expression bx where the base b is  a positive number other than 1.

x

Feb 25­3:18 PM

1.  Make a table of values:

Graph f(x)=2

What did you observe? • •

y=2x

• 2.  Y­Intercept



3.  Notice the end behavior of the graph:

x→  f(x)→  x→­  f(x)→  4.  An Asymptote is a line that a graph  approaches as you move away from the origin.

y=

Feb 25­3:18 PM

Feb 25­3:24 PM

1

Exponential GROWTH Function:

y=abx

Graph   y = ­ (3/2)x

if a>0 and b>1.   **Same characteristics of the graph 7=a*2x.

•Graph y = (½) 3x • Plot (0, ½) and (1, 3/2) • Then, from left to right, draw a curve that  begins just above the x­axis, passes thru the 2  points, and moves up to the right

Feb 25­3:34 PM

To graph a general exponential function,

Feb 25­3:40 PM

Graph y=3*2x­2 +1

y=a*bx­h+k Graph y=3*2x­1 ­ 4 1.  Start by sketching the graph of y=3*2x 2. Translate the graph (horizontal and vertical shifts)

Feb 25­3:41 PM

Feb 25­3:44 PM

2

USING EXPONENTIAL GROWTH MODELS When a real­life quantity increases by a fixed percent each year (or other time period), the amount y of  the quantity after t years can be modeled by this equation:

y=a(1+r/n)nt In this model,  • a is the intial amount,  • r is the percent increase expressed as a decimal, and  • n is the number of times the rate is compounded per year. EXAMPLES: • In 1980 wind turbines in Europe generated about 5 gigawatt­hours of energy.  Over the next 15 years,  the amount of energy increased by about 59% per year.  Write a model giving the amount E (in  gigawatt­hours) of energy t years after 1980.

• You buy a commemorative coin for $110.  Each year t, the value V, of the coin increases by 4%.

Feb 25­3:45 PM

3

Graph f(x)=2x

Make a table of values: 2. YIntercept. 3. Notice the end ... In 1980 wind turbines in Europe generated about 5 gigawatthours of energy. Over the next 15 years,.

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