Lesson 1: Exponential Functions
Lesson 2: Inverses of Relations and Functions
Lesson 3 Logarithmic Functions
Lesson 4: Properties of Logarithms
Lesson 5: Exp and Log Eq's
Lesson 6: All about e
Lesson 7: Exp and Log Models
Grab Bag
100
Is this function exponential growth or decay?
f(x)=100(0.9)^x
Exponential decay
100
Write the inverse of the following function:
f(x)=x+5
f^-1(x)=x-5
100
Write the following equation as a log statement:
3^2=9
log_(3)9=2
100
Write as one logarithm, simplify if possible:
log_(2)8+log_(2)4
log_(2)32=5
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
Is the following data exponential? If so, what is the constant ratio?
Not exponential. Linear.
100
What is a group of dolphins called?
A pod
200
Exponential growth or decay:
f(x)=0.3(1+0.4)^x
Exponential growth
200
Write the inverse of the following function:
f(x)=x/7
f^-1(x)=7x
200
Write the log statement as an exponential equation:
log_(5)125=3
5^3=125
200
Write as a single logarithm, simplify if possible:
log_(4)1024-log_(4)64
log_(4)16=2
200
Solve:
5^x=10
x~~1.43
200
Simplify:
ln(e)^2
2
200
Is the following data exponential? If so, what is the constant ratio?
Exponential! Constant ratio: 3
200
What is the smallest planet in the solar system?
Mercury
300
In 1947, a New York investor invested $20,000 in a company stock that pays returns at 13% each year. Write a function that models this growth.
A(t)=20000(1.13)^t
300
Write the inverse of the following function:
f(x)=4x-1
f^-1(x)=(x+1)/4
300
Write the log statement as an equation:
log30=x
10^x=30
300
Evaluate:
log_(5)25^2
log_(5)25^2=4
300
Solve
log_2(x+4)=log_2(2x)
x=4
300
Simplify:
e^(ln(x)
x
300
Create a natural logarithmic model from the following data:
y=2.1+4.16ln(x)
300
What is a math teacher's favorite dessert?
Pie!
400
If I bought a car for $30,000 in 2010, and it depreciates in value by 10% each year, what will the cars value be in 2025?
~~$6176
400
Graph the relation and connect the points. Then, graph the inverse.
400
Evaluate using mental math:
log_(3)27
log_(3)27=3
400
Evaluate:
6^(log_6x)
6^(log_6x)=x
400
Solve:
log_5(2x)=3
x=62.5
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 in 2024?
~~$5473.95
400
Given the following data: Make an exponential model for it and find they value when x = 10.
9536.743
400
What is our body's largest organ?
The skin
500
If you were to buy $3000 of gold in the year 2000, and the gold accumulates 15% of its value per year, what year will it be when the gold is worth $1,000,000?
2042
500
Graph the function, then find and graph the inverse:
f(x)=2x+4
f^-1(x)=(x-4)/2=1/2x-2
500
Evaluate using mental math:
log_(12)(1/12)
log_(12)(1/12)=-1
500
Evaluate:
log_(7)56
(log56)/(log7)~~2.07
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
Determine if the following data is exponential. If it is, then create an exponential model for the data:
Not exponential!
500
What is the deadliest animal in the world?
The mosquito