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.
Feb 253:18 PM
1. Make a table of values:
What did you observe? • •
• 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.
Feb 253:18 PM
Feb 253:24 PM
Exponential GROWTH Function:
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
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