Linear or Exponential
Characteristics of Exponential Functions
Growth vs Decay
Transformations
Writing Exponential Functions
Real World Applications
100
What is the MAIN difference between linear functions and exponential functions?
Linear functions have has a constant rate of change.
Exponential functions have a constant ratio of change.
100
Determine the domain and range of the graph below.
Domain: (-∞, ∞)
Range: (0, ∞)
100
How can a student determine if an equation represents exponential GROWTH or DECAY if the equation form is
y=a*b^x
If b > 1, the function represents exponential growth.
If 0 < b< 1, the equation represents exponential decay.
100
The graphs of an exponential function (red) and a transformed function are shown below. What is the transformation that was performed?
Translated (shifted) down 3 units.
100
Write equation of of the exponential function represented by the yellow triangles.
y = 3x
100
The local animal rescue league is trying to reduce the number of stray dogs in the county. They estimate that there are currently 400 stray dogs and that through their efforts they can place about 8% of the animals each month. Write the equation of the function where x is months and y is the total number of stray dogs.
y=400(.92)^x
200
What is the equation of a Linear vs Exponential Function?
Linear Functions: f(x) = mx + b
Exponential Functions: f(x) = a(b)x
200
What is the y-intercept and horizontal Asymptote of the following function?
y-intercept: (0, -2)
asymptote: y = -4
200
Describe the following functions as Growth or Decay and Increasing or Decreasing
a) exponential decay / deceasing function
b) exponential growth / increasing function
c) exponential growth /decreasing function
200
The graphs of an exponential function (red) and a transformed function are shown below. What is the transformation that was performed?
Vertically stretched by a factor of 4.
200
What is the function represented by the image?
y=2^x
200
If you tell a rumor to 3 friends on the first day, and those people each tell 3 other friends on the second day, who then tell 3 more friends on the 3rd day, etc. How many people will hear this rumor on the 8th day?
y=3^8
6561 people
300
Select all equations that are NOT exponential functions:
A. f(x) = 5x D. f(x) = 2x-1
B. y =4x E. y = 7.1x
C. y = 2(4)x F. f(x) = 2/5x + 3
B D F
300
Give the initial value, horizontal asymptote, domain and range of the following function?
Initial value: 4 (y-intercept)
Asymptote: y = 2
Domain: (-∞, ∞), Range: (2, ∞)
300
Describe the following functions as Growth or Decay and Increasing or Decreasing.
a) exponential decay / decreasing function
b) exponential decay / increasing function
c) exponential growth / increasing function
300
The graphs of two exponential functions are shown and are in the form a(b)^x+k . Which value must be different? Is this a transformation?
The base, b, is different.
No, these are 2 different parent functions.
300
Write equation of of the exponential function represented by the graph below.
y=-4^x
300
College tuition is out of control increasing by 4% per year. If the current college tuition of your dream college is $58000, what will be the college tuition when you enter college (to the nearest dollar)?
y=58000(1.04)^x
Current 8th graders: 58000(11.04)^5 = $70566
Current 7th graders: 58000(11.04)^6 = $73389
400
Is the function represented below Linear or Exponential?
What is the common rate or ratio?
Linear function
constant rate of change: m = 3
400
What is the general formula for exponential functions?
y=abx
400
f(x)=.25(1.3)x
Does this functions represent exponential growth or decay? What is the percent growth/decay rate?
Exponential Growth
30%
400
The graphs of two exponential functions are shown below in the form a(b)^x+k . What is the transformation from the red graph to the blue graph?
Reflected over the x-axis and translated down 3 units
400
Write equation of of the exponential function represented by the table below.
j(m) = 1.2(1/2)^m
400
If you don’t brush your teeth regularly, it won’t take long for large colonies of bacteria to grow in your mouth. Suppose a single bacterium lands on your tooth and starts multiplying by a factor of 4 every hour.
How many bacteria will be in the colony after 7 hours?
y=4^7
16384 bacteria
500
Is the function represented below Linear or Exponential?
What is the common rate or ratio?
Exponential Function
Common ratio: b = 0.7
500
What make a function an exponential function?
The equation has the variable in the exponent.
500
f(x)=a(0.93)x
Does this functions represent exponential growth or decay? What is the percent growth/decay rate?
f(x)=a(0.93)x
Does this functions represent exponential growth or decay? What is the percent growth/decay rate?
500
Which, if any, single transformation of an exponential parent function would change the domain, range, or asymptote.
Dialation: No change in domain, range or asymptote
Reflection: Changes range only
Translation: Changes range and asymptote
500
Write equation of of the exponential function represented by the graph below.
y=5*2^x
500
The value of a new car depreciates (decreases) exponentially after it is purchased. Suppose that the value of the car is $12000 at the end of 5 years and that its value has been decreasing at the rate of 9% per year. Find the value of the car when it was new.
12000=a(.91)^5
a=$19239.77