Transcript Graph Exponential Decay Functions

Five-Minute Check (over Chapter 6)
CCSS
Then/Now
New Vocabulary
Key Concept: Parent Function of Exponential Growth Functions
Example 1: Graph Exponential Growth Functions
Key Concept: Transformations of Exponential Functions
Example 2: Graph Transformations
Example 3: Real-World Example: Graph Exponential Growth
Functions
Key Concept: Parent Function of Exponential Decay Functions
Example 4: Graph Exponential Decay Functions
Example 5: Real-World Example: Graph Exponential Decay
Functions
Over Chapter 6
Solve 4a2 – 9 = 0.
A. ± 1
3
B. ± __
2
C. ± 2
2
D. 2, __
3
Over Chapter 6
Solve 6y3 + 13y2 + 5y = 0.
A. 3, 2, 1
B.
C.
D.
Over Chapter 6
Find (f + g)(x) if f(x) = 3x + 7 and g(x) = x2 – 10.
A. (f + g)(x) = 3x2 – 70
B. (f + g)(x) = x2 + 3x – 3
C. (f + g)(x) = x2 – 3x + 17
D. (f + g)(x) = 3x – 3
Over Chapter 6
Determine whether f(x) = 4x – 9 and g(x) =
are inverse functions.
A. yes
B. no
Over Chapter 6
A. –9xy2
B. –9x2y4
C. –3xy2
D. 3xy2
Over Chapter 6
A. –7
B.
C. –2
D. 4
Content Standards
F.IF.7.e Graph exponential and logarithmic
functions, showing intercepts and end behavior,
and trigonometric functions, showing period,
midline, and amplitude.
F.IF.8.b Use the properties of exponents to
interpret expressions for exponential functions.
Mathematical Practices
3 Construct viable arguments and critique the
reasoning of others.
You graphed polynomial functions.
• Graph exponential growth functions.
• Graph exponential decay functions.
• exponential function
• exponential growth
• asymptote
• growth factor
• exponential decay
• decay factor
Graph Exponential Growth Functions
Graph y = 4x. State the domain and range.
Make a table of values. Connect the points to sketch a
smooth curve.
Graph Exponential Growth Functions
Answer:
The domain is all real numbers, and the range is all
positive real numbers.
Which is the graph of y = 3x?
A.
B.
C.
D.
Graph Transformations
A. Graph the function y = 3x – 2. State the domain
and range.
The equation represents a translation of the graph
y = 3x down 2 units.
Graph Transformations
Answer:
Domain = {all real numbers}
Range = {y│y > –2}
Graph Transformations
B. Graph the function y = 2x – 1. State the domain
and range.
The equation represents a translation of the graph
y = 2x right 1 unit.
Graph Transformations
Answer:
Domain = {all real numbers}
Range = {y │y ≥ 0}
A. Graph the function y = 2x – 4.
A.
B.
C.
D.
B. Graph the function y = 4x – 2 + 3.
A.
B.
C.
D.
Graph Exponential Growth
Functions
INTERNET In 2006, there were 1,020,000,000
people worldwide using the Internet. At that time,
the number of users was growing by 19.5%
annually. Draw a graph showing how the number
of users would grow from 2006 to 2016 if that rate
continued.
First, write an equation using a = 1.020 (in billions),
and r = 0.195.
y = 1.020(1.195)t
Then graph the equation.
Graph Exponential Growth
Functions
Answer:
CELLULAR PHONES In 2006, there were about
2,000,000,000 people worldwide using cellular phones.
At that time, the number of users was growing by 11%
annually. Which graph shows how the number of users
would grow from 2006 to 2014 if that rate continued?
A.
B.
C.
D.
Graph Exponential Decay Functions
A. Graph the function
and range.
State the domain
Graph Exponential Decay Functions
Answer:
Domain = {all real numbers}
Range = {y│y > 0}
Graph Exponential Decay Functions
B. Graph the function
domain and range.
State the
The equation represents a transformation of the graph
of
Examine each parameter.
● There is a negative sign in front of the function:
The graph is reflected in the x-axis.
● a = 4: The graph is stretched vertically.
Graph Exponential Decay Functions
● h = 1: The graph is translated 1 unit right.
● k = 2: The graph is translated 2 units up.
Answer:
Domain = {all real numbers}
Range = {y│y < 2}
A. Graph the function
A.
B.
C.
D.
B. Graph the function
A.
B.
C.
D.
Graph Exponential Decay
Functions
A. AIR PRESSURE The pressure of the atmosphere
is 14.7 lb/in2 at Earth’s surface. It decreases by
about 20% for each mile of altitude up to about
50 miles. Draw a graph to represent atmospheric
pressure for altitude from 0 to 20 miles.
y = a(1 – r)t
= 14.7(1 – 0.20)t
= 14.7(0.80)t
Graph Exponential Decay
Functions
Graph the equation.
Answer:
Graph Exponential Decay
Functions
B. AIR PRESSURE The pressure of the atmosphere
is 14.7 lb/in2 at Earth’s surface. It decreases by
about 20% for each mile of altitude up to about
50 miles. Estimate the atmospheric pressure at an
altitude of 10 miles.
y = 14.7(0.80)t
Equation from part a.
= 14.7(0.80)10
Replace t with 10.
≈ 1.58 lb/in2
Use a calculator.
Answer: The atmospheric pressure at an altitude of
about 10 miles will be approximately
1.6 lb/in2.
A. AIR PRESSURE The pressure of a car tire with a bent rim
is 34.7 lb/in2 at the start of a road trip. It decreases by about
3% for each mile driven due to a leaky seal. Draw a graph to
represent the air pressure for a trip from 0 to 40 miles.
A.
B.
C.
D.
B. AIR PRESSURE The pressure of a car tire with a
bent rim is 34.7 lb/in2 at the start of a road trip. It
decreases by about 3% for each mile driven due to
a leaky seal. Estimate the air pressure of the tire
after 20 miles.
A. 15.71 lb/in2
B. 16.37 lb/in2
C. 17.43 lb/in2
D. 18.87 lb/in2