1. Growth Factor (b) = 1 ± Growth Rate (r)
Starter
Thursday
February 12, 2015
Give the mathematical model for the situation that has the following growth factor/growth rate and given initial amount.
1. Growth factor: 3
2. Growth rate: 9.2%
Initial value: 1 2
Initial value: 2
Remember:
Growth Factor (b) = 1 ± Growth Rate (r)

2. The answer looks like this:
Logarithm Equations
What is an Exponent?
2 3
What is a Logarithm?
A logarithm goes the other way. It asks, “what exponent produced this?”
exponent
base
The exponent of a number says how many times to use the number in a multiplication.
2 ? = 8
The answer looks like this:
𝐥𝐨𝐠 2 8 =3
2 3 =2∗2∗2
2 3 = 8
Exponents and Logarithms:
“undo” each other (as long as they have the same base)
Are inverses of each other

3. Logarithm Equations Rewrite each equation in exponential form:
2 3 = 8
𝐥𝐨𝐠 2 8 =3
Rewrite each equation in exponential form:
Rewrite each equation in logarithmic form:
log 3 x =4
log y 2 =5
log 1 y =x
log 30 =x
4 3 =64
3 x =27
8 0 =1
x= y −12

4. Natural Logarithm Write in exponential form:
𝑒 𝑥
𝐥𝐨𝐠 𝑒 𝑥
When the base is e, we get:
The Natural Logarithm 𝐥𝐨𝐠 𝑒 𝑥
Also knowns as ln(𝑥)
Write in exponential form:
5. ln 𝑦=𝑥
6. ln 𝑥=15
Write in logarithmic form:
5. 𝑒 15 =𝑥
6. 𝑒 𝑛 =3

5. Evaluating log 3 9 log 2 16 log 4.1 log 2 32 log 2 32 = log 32 log 2
2 3 = 8
𝐥𝐨𝐠 2 8 =3
Evaluate each expression without a calculator.
log 3 9
log 2 16
Evaluate each expression WITH a calculator.
log 4.1
log 2 32
Enter in the calculator like this:
log = log 32 log 2
log 37