Definition: If n is a positive integer an x is a numerical base, then
(n times)Exponential Rules
Radicals as Exponents
Exponential Functions
- Standard form of an exponential function is f(x)= a
, where b>0, b
1 and a is the y intercept.
Red - When x is a negative exponent
Blue - When x is a positive exponent2. Shifting the Graph:
g(x) = f(x-2) shift 2 righth(x) = f(x) - 2 shift 2 down
j(x) = -f(x) reflection in the x axis
Radioactive Decay
t = time, m = initial mass, h = half life
Natural Base e
- e is a irrational number and is derived from computation:
- e can be approximated using the following expression:
- To imput into your calcuter, hit 2nd LN
Compounding Countinuously
Logarithm- An exponent
(log to the base a of x)
Properties of logs
Log base e (ln)
a=ln(a)
Change of Base Formula
Exponential Function
The inverse of y=
is y=
x------------------------------------------------------------------------------------------------
Example Questions:
Unless other directions are given, solve for x:
- Expand
as a function of individual logs. 
- Graph
- Given
, for what value of t will P be greater than 200,000? (round to the thousandth.) 
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Answers
1)
2) x = 119.89
3) x = 2.77
4) x = 1.54
5) 3 ln(x) - (2 ln(y) +5 ln(z))
6) x = 7
7)
8) x = -1, x = 5
9) t = 24.26
10) x = 9
1)
2) x = 119.89
3) x = 2.77
4) x = 1.54
5) 3 ln(x) - (2 ln(y) +5 ln(z))
6) x = 7
7)
8) x = -1, x = 5
9) t = 24.26
10) x = 9
2 comments:
Good start!
I like how you were able to include some screenshots of pdf's downloaded from Blackboard. Very resourceful.
You need to remove some whitespace from your post!
Your "properties of logs" section is a bit hard to read, and could use some better spacing.
I also think you should include the log laws, for example log(ab) = log a + log b.
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