Exponential Functions
Linear, Quadratic, & Exponential Models
Logarithmic Functions
Solving Exponential Functions
Math Trivia!
100
Exponential growth functions have a base that is __________ one.
greater than
100
Linear models have a line of best fit in the shape of a _______ and quadratic models have a "line" of best fit in the shape of a ___________.
line; parabola
100
What is the inverse function of the exponential function?
The logarithmic function
100
What is the base of the "common log"?
What is the base of the "natural log"?
10; e
100
What mathematical theorem is visualized in the picture below?
Pythagorean Theorem
200
An exponential decay function has a base that is between:
zero and 1
200
A line of best fit can be used to interpolate and extrapolate data. Which of these terms describes a prediction made for values outside of the data set?
extrapolate
200
Exponential functions have horizontal asymptotes. What kind of asymptotes do logarithmic functions have?
Vertical
200
Rewrite the logarithm using the product property:
logb(mn)
logbm+logbn
200
A perfect number is defined as a positive integer that is equal to the sum of its positive divisors other than the number itself. What is the smallest perfect number?
6
300
What is the equation for transformational form of an exponential equation? Describe what the variables a, h, and k all represent.
f(x)=abx-h+k
a: stretch/compression/flip
h: horizontal shift
k: vertical shift
300
If you were to record the value of your Rolex over a period of 10 years, would you expect to use an exponential growth model or an exponential decay model?
Growth
300
Write 53=123 in logarithmic form.
log5125=3
300
Rewrite the logarithm using the power property:
logbmn
nlogbm
300
What is the next number in the series:
1, 3, 6, 10, 15, 21, 28, 36, ...
45
400
Sketch the graph of the exponential decay function with an equation of:
f(x)=-1*(1/2)x-1+3
Include the horizontal asymptote in your sketch.
400
What regression model would you choose for the following data set:
quadratic
400
In the transformational equation of a logarithm,
f(x)=alogb(x-h)+k
which variable gives the vertical asymptote?
h
400
Evaluate the logarithm using the change of base property:
log912+log9546+.75
4
400
In geometry, a curve known as a "lemniscate" most closely represents the shape of what single digit number?
8
500
Write an equation for the graph below:
f(x)=2x-2-1
500
Plot the following values on your graphing calculator, fit an exponential regression equation to the data, then give the formula of the regression model.
L1: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
L2: 95.3, 55.9, 23.7, 16.4, 8.8, 4.8, 3.3, 1.9, 1.1, 0.6
f(x)=95.3(.058)x
500
In a logarithmic function, the input is a number and the output is an ______.
exponent
500
Solve the exponential equation:
-6*15^(k-10)=-54
10.6616
500
How many sides does a tetradecagon have?
HINT: The sum of its interior angles is 2160 degrees.
14