12. Base: A number that is multiplied over and over
Exponent:
13. Base: A number that is multiplied over and over
Exponent: Number of factors of the base
14. Base: A number that is multiplied over and over
Exponent: Number of factors of the base
7
x
15. Base: A number that is multiplied over and over
Exponent: Number of factors of the base
7
x = x•x•x•x•x•x•x
16. Example 1
Matt Mitarnowski drives to school. Suppose there is a
probability D that he will run into a delay on the way.
a. What is the probability y that he will be delayed four days
in a row?
17. Example 1
Matt Mitarnowski drives to school. Suppose there is a
probability D that he will run into a delay on the way.
a. What is the probability y that he will be delayed four days
in a row?
y = D•D•D•D
18. Example 1
Matt Mitarnowski drives to school. Suppose there is a
probability D that he will run into a delay on the way.
a. What is the probability y that he will be delayed four days
in a row?
4
y = D•D•D•D = D
19. Example 1
Matt Mitarnowski drives to school. Suppose there is a
probability D that he will run into a delay on the way.
a. What is the probability y that he will be delayed four days
in a row?
4
y = D•D•D•D = D
b. Make a table for D = {.1, .2, .3, ..., .9, 1}
20. Example 1
Matt Mitarnowski drives to school. Suppose there is a
probability D that he will run into a delay on the way.
a. What is the probability y that he will be delayed four days
in a row?
4
y = D•D•D•D = D
b. Make a table for D = {.1, .2, .3, ..., .9, 1}
21. Example 1
Matt Mitarnowski drives to school. Suppose there is a
probability D that he will run into a delay on the way.
a. What is the probability y that he will be delayed four days
in a row?
4
y = D•D•D•D = D
b. Make a table for D = {.1, .2, .3, ..., .9, 1}
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D
y 0.0001 0.0016 0.0081 0.0256 0.0625 0.1296 0.2401 0.4096 0.6561 1
22. Example 1
Matt Mitarnowski drives to school. Suppose there is a
probability D that he will run into a delay on the way.
a. What is the probability y that he will be delayed four days
in a row?
4
y = D•D•D•D = D
b. Make a table for D = {.1, .2, .3, ..., .9, 1}
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D
y 0.0001 0.0016 0.0081 0.0256 0.0625 0.1296 0.2401 0.4096 0.6561 1
23. Example 1
c. What value of D will give a probability of .5 that Matt will
be delayed four days in a row?
24. Example 1
c. What value of D will give a probability of .5 that Matt will
be delayed four days in a row?
4
.5 = D
25. Example 1
c. What value of D will give a probability of .5 that Matt will
be delayed four days in a row?
4
.5 = D
This answer is not in our table!
26. Example 1
c. What value of D will give a probability of .5 that Matt will
be delayed four days in a row?
4
.5 = D
This answer is not in our table!
We need to take a 4th root of D.
27. Example 1
c. What value of D will give a probability of .5 that Matt will
be delayed four days in a row?
4
.5 = D
This answer is not in our table!
We need to take a 4th root of D.
4
4 4
.5 = D
28. Example 1
c. What value of D will give a probability of .5 that Matt will
be delayed four days in a row?
4
.5 = D
This answer is not in our table!
We need to take a 4th root of D.
4
4 4
.5 = D
D ≈ .8408964153
43. Properties of Power
Functions
1. The graph goes through the origin
n
0 = 0 for all n > 0
44. Properties of Power
Functions
1. The graph goes through the origin
n
0 = 0 for all n > 0
2. The domain is all real numbers
45. Properties of Power
Functions
1. The graph goes through the origin
n
0 = 0 for all n > 0
2. The domain is all real numbers
Any number can be taken to an exponent
46. Properties of Power
Functions
1. The graph goes through the origin
n
0 = 0 for all n > 0
2. The domain is all real numbers
Any number can be taken to an exponent
3. The range has two possibilities:
47. Properties of Power
Functions
1. The graph goes through the origin
n
0 = 0 for all n > 0
2. The domain is all real numbers
Any number can be taken to an exponent
3. The range has two possibilities:
a. If n is odd, R = {y: y is all real numbers}
48. Properties of Power
Functions
1. The graph goes through the origin
n
0 = 0 for all n > 0
2. The domain is all real numbers
Any number can be taken to an exponent
3. The range has two possibilities:
a. If n is odd, R = {y: y is all real numbers}
b. If n is even, R = {y : y ≥ 0}
51. Properties of Power
Functions
4. Symmetry exists in 2 cases:
a. If n is odd, there is rotational symmetry about
the origin
52. Properties of Power
Functions
4. Symmetry exists in 2 cases:
a. If n is odd, there is rotational symmetry about
the origin
b. If n is even, there is reflection symmetry over
the y-axis
