Unit 9: Growing, Growing, Growing Name: ______
1.1/1.2: Introducing Exponential Functions
Exponential Form: A quantity expressed as a number raised to a power. Inexponential form, 32 can be written as25. Theexponential formof the prime factorization of 5,000 is23×54.
Exponent: The small raised number that tells how many times a factor is used. For example,53 means5 × 5 × 5. Theexponentis 3.
Base: The number that is raised to a power in an exponential expression. In the expression35, read “3 to the fifth power”, 3 is thebaseand 5 is the exponent.
Standard Form: The most common way we express quantities. For example, 27 is the standard formof33.
Ex: Evaluate
a) 43 = b) 25 = c) 31 =
5.1: Looking for Patterns Among Exponents
x / 1x / 2x / 3x / 4x / 5x5
4
3
2
1
0
-1
-2
-3
5.2: Rules of Exponents
Day #1
Simplify. Write the product as one power.1. 2. 3.
Simplify. Write the quotient as one power.
1. 2. 3.
Simplify.
1. 2. 3.
Day #2
Evaluate1. 30 = 2. 53987630 = 3. x0 =
Simplify negative exponents.
1. = 2. = 3. =
Simplify. Write the answers as one power with no negative exponents.
1. = 2. = 3.
4. 5. = 6. =
Day #3
Simplify. Write the answers without negative exponents.1. 2.
2. 4.
5. 6.
7. 8.
9.
5.4: Scientific Notation
Scientific Notation: A short way to write very large or very small numbers. A number is in scientific notationif it is of the forma × 10n, wherenis an integer and1 ≤ a 10.
Write in standard form.1. 1.35 ´ 105
2. 2.7 ´ 10–3
3. 2.87 ´ 109
4. 1.9 ´ 10–5 / Write in scientific notation.
1. 543000
2. 0.00709
3. 0.000811
Evaluate
1. How many times larger is the diameter of the Sun (1.3 ´ 106 km) compared to the diameter of Earth (1.3 ´ 104 km)?
2. How many times larger is the distance to the Jupiter (7.5 ´ 1010 km) than the distance to Venus (42,000,000)?
5. If the weight of an object in tons is 3.4×104, what would that weight be in pounds (1 ton = 2000 pounds) / Evaluate
1. (2.0 ´ 103) ´ (2.6 ´ 106)
2. (4.10 ´ 1011) ÷ (301,000,000)
3. (4.0 ´ 102) ´ (3.5 ´ 103)
4. (2.0 ´ 106) ÷ (2.5 ´ 102)