Algebra 2
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thoughts here!
9.1 – Exponential Growth
Name:____________________
1
If the variable is not in the ________________, then it is ______ an exponential function.
Initial Value
______________
Growth/decay factor
_________________
Condition 1:
Condition 2: The base ( ) is a positive number other than 1.
Identify if the following functions are exponential. If they are, state the initial value and
the growth/decay factor. If they’re not, explain why not.
Is it exponential?
Is it exponential?
Is it exponential?
Is it exponential?
Is it exponential?
Linear vs. Exponential:
EXPONENTIAL GROWTH FUNCTIONS:
If _______, then the graph will “grow” away from the asymptote as you move left to right.
y
The x-axis
is an
_____________ of the graph. An
asymptote is an imaginary line that
a graph approaches more and
more ________.
x
Domain:
Range:
2
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thoughts here!
Are the following graphs exponential growth functions?
y
y
y
y
x
x
x
x
1. Graph
x
y
Domain:
Range:
For exponential functions that are in the form
the graph will go through:
and
and have an asymptote on the
Try these examples on your own:
2. Graph
Domain:
Range:
axis (that’s the line
)
3. Graph
Domain:
Range:
3
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thoughts here!
TRANSLATIONS
To graph the function above, identify points for the graph of
, and then translate
the graph horizontally (left/right) by ___ units and vertically (up/down) by ___ units.
4. Graph
Domain:
Range:
COMPOUND INTEREST
P = ___________ (initial investment)
r = ________________________
t = ______ (years)
n = the number of times the
interest is ______________ (paid)
per year.
5. You deposit $3,000 in an account that pays 3.28% annual interest. Find the balance
after 5 years if the interest is compounded semi annually. How much would you have if
the interest was compounded daily for five years?
Semi Annually
Daily
9.1 Practice – Exponential Growth
Name: _________________
Next to each function, write “yes” if it is an exponential function. If the answer is “no”, write an
explanation why not.
1)
2)
3)
4)
5)
6)
7)
8)
For 9 14, sketch the graph of each exponential function by doing the following: Sketch the asymptote,
label at least two distinct coordinate points on each graph, and write the domain and range of each
function.
10.
9.
Domain:
Range:
12.
Domain:
Domain:
11.
Range:
13.
Range:
Domain:
Domain:
Range:
14.
Range:
Domain:
Range:
9.1 Application and Extension
1. Write down three coordinate points of the graph for
2. Mr. Brust searches the couches in his classroom every day afterschool to find the loose change that falls
out of his students’ pockets. After one school year, he collected $207. He put this money into an
account for his kids’ college education that pays 4% interest and is compounded monthly.
a. Write a model that represents this situation.
b. Using your model from part a, how much
money will be in the account after 5 years
assuming he puts no more money in? After 20
years?
3. Mr. Sullivan just won a Minecraft design competition and has been awarded $1,000,000!!! The only
catch is he is not allowed to spend any of it for 15 years, but he is allowed to invest it. He found a
Certificate of Deposit account that will pay him 5.25% annual interest compounded daily.
a. Write a model that represents this situation.
b. Using the model, calculate how much interest
he gained during those 15 years.
4. Mr. Kelly has $1,300 to put into a long term account. He found an account that will pay him 9% interest
compounded quarterly.
a. Write a model that represents this situation.
b. How long would it take Kelly to have $10,000 in
his account if he added nothing to it? (Hint:
You have not learned how to solve for a
variable in the exponent yet. Instead, graph the
line
with a graphing calculator.)
c. How long would it take Kelly to have $1 million!!??
9.1 Application and Extension
5. After www.flippedmath.com was created, the number of hits was tracked. The table shows the number
of hits in each of the first 10 months where is the month number.
a. Enter the values into two separate lists on a
graphing calculator.
STEP 1: Hit
and then option 1.
STEP 2: Enter x values into List 1.
STEP 3: Enter y values into List 2.
b. Calculate an exponential model and write the
equation below. (Round to 3 decimals.)
STEP 1: Hit
, then right for the “CALC” menu.
STEP 2: Scroll down until you can choose “ExpReg”
STEP 3: Hit Enter and calculate the “a” and “b”.
y = _________________________
c. According to your model from part b, how
many hits do you expect in the 12th month?
d. According to your model in part b, how many
hits would there be in the 41st month? What is
wrong with this number?
Algebra Skillz:
1. Below are graphs of
(thin line) Simplify the fraction by
rationalizing the
and its translation (bold line). Write an
denominator.
equation of the translation.
y
2.
x
SAT Prep:
1. Simplify:
(A)
(B)
(C)
(D)
Solve by factoring.
4.
3.
2. If
5.
, find
.