Key Features
Growth vs Decay
Exponential Modeling
Transformations
Miscellaneous
100
What is the domain of the function?
(-oo,oo)
100
Is this a growth or decay function?
Growth
100
What is the initial value of this function?
f(x)=30(2)^x
30
100
What is the parent function?
g(x)=2(5)^(x-1)+7
f(x)=5^x
100
How can we tell whether something is a growth vs a decay function?
Growth functions grow or have a growth factor bigger than 1.
Decay functions get smaller or have a growth factor less than 1.
200
What is the range of the function below?
(-2,oo)
200
Is this a growth or a decay function?
g(x)=5(e)^(2x)
Growth.
200
What is the growth factor of the function below?
m(r)=1/2(3)^r
3
200
What are the transformations of the functions before?
h(x)=3(1/2)^x-4
Vertical Stretch BAFO 3
Vertical Shift Down 4 Units
200
What is e? Write the name of e and you have to pronounce it correctly.
Euler's number.
300
What is the horizontal asymptote of the function?
y=-2
300
Is this function growth or decay?
Decay
300
How much bacteria will there after 3 hours. This equation b(t) gives the amount of bacteria after t hours.
b(t)=2(4)^t
128 bacteria.
300
What are the transformations of the function below?
m(t)=2/3(e)^(x-1)-4
Vertical compressions BAFO 2/3
Shift Right 1 Unit
Shift Down 4 Units
300
What does each component of a general expoential function represent?
y=a(b)^x
a: Initial value
b: Growth factor
x: Input
y: Output
400
What is the y-intercept?
(0,-1.5)
400
Is this function a growth or decay?
f(t)=10(5/4)^-x+2
Decay.
400
Isaac has a loan of $10000, every year he will pay off 50% of it. How many years will it take for him to have only $1000 left. Round to the nearest year and make sure it makes sense in context.
4 years.
400
What are the transformations of the function below.
p(r)=pi(3)^(x-2.5)+e
Vertical Stretch BAFO Π (pi)
Shift Right 2.5 Units
Shift Up e Units
400
Write an exponential function that decreases by 25% per year.
Example:
f(x)=5(.75)^x
500
What is the end behavior of the function below?
"as x--->"-oo, " y--->____"
"as x--->"oo, " y--->____"
500
Is this a growth or a decay function?
f(x)=5(1)^(x-2)+3
Neither.
500
Create an equation that fits the description.
Jonathan invests in stocks with a value of $200, every year the value increases by 12%.
f(t)=200(1.12)^t
500
Create a function that fits the description.
An exponential function with a base of .5, reflection across the x-axis, vertical compression BAFO 1/2, Shift left 3 units, and shift down 6 units.
f(x)=-1/2(.5)^(x+3)-6
500
Create a story for the given exponential function. You get 1 attempt.
m(t)=2000(1.15)^t
Timmy buys a pizza place for $2000, the value increases by 15% every year.