4.5: Exp and Log Equations
4.6: The Natural Base, e
4.7: Transformations of Exp and Log Functions
4.8: Curve Fitting with Exp and Log Models
Grab Bag
100
Solve:
9^x=3^(x-2)
x=-2
100
What is the decimal approximation of e to the nearest hundredth
e~~2.72
100
Describe the transformations of the following function from its parent function:
g(x)=2^x-7
Vertical shift down 7
100
Is the following data exponential? If so, what is the constant ratio?
Not exponential, linear!
100
What band released the song Let It Be in 1970?
The Beatles
200
Solve:
5^x=10
x~~1.43
200
Simplify:
ln(e)^2
2
200
Describe the transformations of the following function from its parent function:
f(x)=log(3x)
Horizontal compression by a factor of
1/3
200
Is the following data exponential? If so, what is the constant ratio?
Exponential! Constant ratio: 3
200
What year did we first land on the moon?
1969
300
Solve:
log_2(x+4)=log_2(2x)
x=4
300
Simplify:
e^(5ln(x)
x^5
300
Describe all of the transformations applied to the following function from its parent function:
g(x)=3(2^(x+1))
Vertical stretch by a factor of 3
Horizontal shift left by 1
300
Create a natural logarithmic model from the following data:
y=2.1+4.16ln(x)
300
What month of the year has 28 days?
All of them!
400
Solve:
x=2
x=2
400
In 1990, Mr. Willbanks deposited $1000 into a bank account that earns 5% interest compounded continuously. How much money would be in the account today?
~~$5473.95
400
Take the function f(x)=2^x and apply the following transformations:
Vertical compression x 1/2 ,
Reflection across y-axis
g(x)=1/2(2^-x)
400
Given the following data: Make an exponential model for it and find the x value for when y = 10 (use Desmos)
y=2.5^x
400
Who was the 3rd president of the United States?
Thomas Jefferson
500
Solve:
1.5^(x-1)=14.5
x~~7.60
500
At some point in the distant past, Mr. Poling opened a bank account with $300 that earns 3% interest that is compounded continuously. If the account has $470.49 in it today, how many years ago was the account opened?
15 years
500
Take the function f(x)=log(x) and apply the following transformations:
Horizontal shift right 5
Vertical shift down 4
Reflection across x-axis
g(x)=-log(x-5)-4
500
Determine if the following data is exponential. If it is, then create an exponential model for the data:
Not exponential!
500
What is "hi" in the middle and round on both ends?
Ohio!
