Transcript Chapter 7 7.1

7-1
Exponential Functions, Growth, and Decay
WARM-UP
Evaluate the following expressions:
1.2-3
2.
50
3.
10(1-.75)2
Find the values indicated using the graph:
4. f(2) = _____
5.
f(___) = 4
LEARNING GOALS – LESSON 7.1
Write and evaluate exponential expressions to model growth and
decay situations.
In case of a school closing, the principal calls 3 teachers.
Each of these teachers calls 3 other teachers and so on. How
many teachers will have been called in the 4th round of calls?
Draw a diagram to
show the number of
Teachers called in each
round of calls.
_____________
_____________
_____________
* Notice that after each round of calls the number
of families contacted is a power of 3.
Write a function to represent this situation where y is the
number of people contacted and x is the round number.
Holt Algebra 2
7-1
Exponential Functions, Growth, and Decay
What does the following phrase mean in your own words?
“The number of transistors required per circuit has increased
exponentially since 1965.”
Check out the y-values. What pattern do you notice?
Growth that ______________ every year can be modeled by an
_______________ function.
The parent exponential function: f(x) = bx, where x is the variable.
When something doubles the b value will be ______.
What about when it triples?
Holt Algebra 2
7-1
Exponential Functions, Growth, and Decay
The graph of the parent function: f(x)= 2x
is shown.
Domain : { R } all _______ numbers
Range : {y|y > 0} all ________ numbers
The function never reaches the x-axis because the value of 2x≠0 ever.
In this case, the x-axis is an ____________________.
Exponential Growth
Exponential Decay
f(x) = abx
f(x) = abx
• a > 0 (_____________)
•a > 0 (_____________)
•b > 1 (_________ than 1)
•0 < b < 1 (____________ 0 and 1)
As x increases y ________________
As x increases, y ________________
Holt Algebra 2
7-1
Exponential Functions, Growth, and Decay
Example 1A: Graphing Exponential Functions
Tell whether the function shows growth or decay.
Then graph.

f(x)  10
3
4
x
Step 1 Find the value of the base.
• Determine if it represents growth or decay.
Step 2 
Graph the function by using a table of values.
• Determine appropriate x values.
• Plug function into graphing calculator and use table
feature to fill in chart.
x
f(x)
• Graph.
Check by graphing in
calculator. Be sure to
appropriately represent
asymptotes!
Holt Algebra 2
7-1
Exponential Functions, Growth, and Decay
Example 1B: Graphing Exponential Functions
Tell whether the function shows growth or decay.
Then graph.
g(x) = 100(1.05)x
Step 1 Is this GROWTH or DECAY ? (Circle One)
Step 2 PREPARE TO GRAPH the function by making a table of
values.
x
f(x)
Exponential Growth/Decay (at a constant rate)
What do you think the ± tells us about the formula?
+ means ____________
Holt Algebra 2
and
– means ______________
7-1
Exponential Functions, Growth, and Decay
Example 2: Biology Application
In 1981, the Australian killer whale population was 350
and increased at a rate of 14% each year since then. Use a
graph to predict when the population will reach 20,000.
Step 1: Determine if this problem
is representing a growth or
decay; write the general formula.
Step 2: Substitute in the info that you have.
Step 3: Since you don’t know how to solve for t yet (because
it is an exponent) graph it and using the [TRACE]
feature estimate what value of t (x) will give you 20,000 (y).
Step 4: Be sure to use the t value that you found to count years
past 1981 to give the year the population will reach 20,000.
Holt Algebra 2
7-1
Exponential Functions, Growth, and Decay
Example 3: Depreciation Application
A city population, which was initially 15,500, has been
dropping 3% a year. Write an exponential function and
graph the function. Use the graph to predict when the
population will drop below 8000.
Step 1 Determine if this problem is representing a growth or
decay; write the general formula.
Step 2
Substitute in the information that you have.
Step 3 Since you don’t know how to solve for t yet (because
it is an exponent) graph it and using the [TRACE] feature
estimate what value of t (x) will give you a number just below
8,000 (y).
Holt Algebra 2