Graphing Exponential Functions
Solving Exponential Equations
The Natural Base, e
Geometric Sequences
Modeling Data and Random Trivia
100
Given the following equation,
y=a(b)^(x-h)+k
Which letter determines exponential growth or exponential decay?
b
100
729=3^x
x=6
100
The natural base, e, is similar to what over irrational constant?
pi
100
This is the difference between arithmetic and geometric sequences.
You add a common difference in arithmetic sequences and you multiply a common ratio in geometric sequences.
100
A university in Northern California has a mascot that is named this, after the color, not the bird.
Cardinal - Stanford University
200
Does the following equation represent exponential growth or exponential decay?
y=2(0.92)^x-3
Exponential decay
200
6^(5x-9)=36^x
x=3
200
What is the approximate value of the natural base, e, to the thousandths place?
e =2.718
200
Which of the following graphs show a geometric sequence?
A.
B.
C.
D.
Graph C
200
Using a graphing calculator, is the following table best represented by a linear, quadratic, or exponential function?
Linear function
300
Chris states that the following graph shows exponential decay because the graph is decreasing,
is his statement true?
No, it is exponential growth reflected across the x-axis.
300
11^(5x+3)=11^(3x-13)
x=-8
300
The value of an investment after t years is given by the equation,
A=1250e^(0.085*t)
What does the value 0.085 represent?
The interest rate
300
Write an equation for the nth term of the geometric sequence below,
1/4, 3/20, 9/100, 27/500, ...
an=1/4(3/5)^(n-1)
300
This US President was a failed cattle rancher, naval history scholar, widower, the New York City Police Commissioner, Governor of New York, Army Colonel, Harvard Grad and Columbia Law School Student all before his Vice-Presidency at the age of 42.
Who is Theodore Roosevelt.
400
Given the following table of values,
Does the table show exponential growth or exponential decay?
Exponential Growth
400
(1/4)^x=256
x=-4
400
A corn stalk is planted in Iowa and begins growing. The height of the corn stalk in centimeters, H, is given by the equation,
H=2e^(0.05*t)
where t is the number of days after planting.
How tall is the corn stalk after 90 days in centimeters.
H=180.03
400
Lauren puts $500 in a savings account to have a college graduate party, which each year yields 4% interest on the amount she has currently saved. If she starts the account just before she begins her 4-year college degree, how much will the account have when she graduates?
$584.93
400
This is the name of the boat in the movie Jaws.
The Orca
500
The parent function,
y=2^x
is given by the red graph.
What equation represents the blue graph?
y=2(2)^(x-3)+4
500
6^(-6x+6)=(1/216)^(x+1)
x=-3
500
Sarah places a hot pizza on her kitchen counter and measures the temperature in Fahrenheit, T, after m minutes. She graphs the temperatures and times to get the following equation:
T=42+82e^(-0.045*m)
She makes five statements based on the equation. Which of these statements are true?
1. The temperature of the pizza is increasing.
2. The y-intercept of the function is (0,265).
3. The temperature of the pizza is 265 degrees out of the oven.
4. The temperature of the pizza approaches 42 degrees over time.
5. The temperature of the pizza is decreasing.
Statements 2, 3, 4, and 5 are true.
500
Mr. T writes a geometric sequence on the board,
Determine the position n, of the term an=
1/(120,932,352)
n=13
500
9 Bubbles