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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.
Graph Transformations
A. Graph the function y = 3x – 2. State the domain and range.
The equation represents a translation of the graphy = 3x down 2 units.
Graph Transformations
B. Graph the function y = 2x – 1. State the domain and range.
The equation represents a translation of the graphy = 2x right 1 unit.
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.
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
The equation represents a transformation of the graph
of
B. Graph the function State the domain and range.
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
Answer:
Domain = {all real numbers}
Range = {y│y < 2}
● h = 1: The graph is translated 1 unit right.
● k = 2: The graph is translated 2 units up.
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
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 ofabout 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.
A. 15.71 lb/in2
B. 16.37 lb/in2
C. 17.43 lb/in2
D. 18.87 lb/in2
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.