8.1 Exponents axax exponent base means a a a … a x times

8.1 Exponents Rules For Exponents and Scientific Notation If a > 0 and b > 0, the following hold true for all real numbers x and y.

8.1 Exponents 4 2 · · (x2)5(x2)5 x 10 (x 2 )(x 9 )x 11 (a2b3)7(a2b3)7 a 14 b 21 (3a 3 b 5 ) 4 81a 12 b 20

For any nonzero number x: and 8.2 Negative Exponents

For any nonzero number x: 8.2 Negative Exponents

Examples: 8.2 Negative Exponents

If we apply the quotient rule, we get: 8.3 Division Property of Exponents

Scientific notation is used to express very large or very small numbers. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10. The number has one digit to the left of the decimal point. The power of ten indicates how many places the decimal point was moved Scientific Notation

= 5.5 x 10 6 We moved the decimal 6 places to the left. A number between 1 and 10

8.4 Scientific Notation = 7.5 x We moved the decimal 3 places to the right We moved the decimal 3 places to the right. A number between 1 and 10 Numbers less than 1 will have a negative exponent.

8.4 Scientific Notation CHANGE SCIENTIFIC NOTATION TO STANDARD FORM 2.35 x 10 8 = 2.35 x = Standard form Move the decimal 8 places to the right

8.4 Scientific Notation 9 x = 9 x = Move the decimal 5 places to the left Standard form

8.4 Scientific Notation Express in scientific notation 1) ) ) )

8.4 Scientific Notation Change to Standard Form 1) 4.21 x ) 0.06 x ) 5.73 x ) x 10 -5

Scientific Notation 7,000,000,000 = 7 billion = 7 x ,000,000 = 7 million = 7 x Scientific Notation

Scientific Notation 7,240,000 = 7.24 million = 7.24 x = 345 ten thousandths = 3.45 x Scientific Notation

Adding and Subtracting Exponents and Scientific Notation must be the same! (1.2 x 10 6 ) + (2.3 x 10 5 ) change to (1.2 x 10 6 ) + (0.23 x 10 6 ) = 1.43 x Scientific Notation

Multiplying Add Exponents and Scientific Notation (3.1 x 10 6 )(2.0 x 10 2 ) = 6.2 x Scientific Notation

Dividing Subtract Exponents and Scientific Notation (3.8 x 10 6 ) (2.0 x 10 2 ) = 1.9 x Scientific Notation

8.4 Problem Solving The distance from the earth to the sun is 1.5 x m The speed of light is 3 x 10 8 m/s. How long does it take for light from the sun to reach the earth?

8.4 Problem Solving The mass of an electron is 9.11 x kg and the mass of a proton is 1.67 x kg. How many times bigger is the proton than the electron?

8.4 Problem Solving How old are you in seconds?

Dividing Subtract Exponents and Scientific Notation (3.8 x 10 6 ) (2.0 x 10 2 ) = 1.9 x Scientific Notation

Dividing Subtract Exponents and Scientific Notation (3.8 x 10 6 ) (2.0 x 10 2 ) = 1.9 x Scientific Notation

If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by the equation Where C = initial amount r = growth rate (percent written as a decimal) t = time where t > 0 (1+r) = growth factor where 1 + r > Compound Interest and Exponential Growth

You deposit $1500 in an account that pays 2.3% interest compounded yearly, 1)What was the initial principal (P) invested? 2)What is the growth rate (r)? The growth factor? 3)Using the equation A = P(1+r) t, how much money would you have after 2 years if you didn’t deposit any more money? 1)The initial principal (P) is $ )The growth rate (r) is The growth factor is Compound Interest and Exponential Growth

If a quantity decreases by the same proportion r in each unit of time, then the quantity displays exponential decay and can be modeled by the equation Where C = initial amount r = growth rate (percent written as a decimal) t = time where t > 0 (1 - r) = decay factor where 1 - r < Exponential Growth and Decay

1)The initial investment was $22,500. 2)The decay rate is The decay factor is Exponential Growth and Decay You buy a new car for $22,500. The car depreciates at the rate of 7% per year, 1.What was the initial amount invested? 2.What is the decay rate? The decay factor? 3.What will the car be worth after the first year? The second year?

1)Make a table of values for the function using x- values of –2, -1, 0, 1, and 2. Graph the function. Does this function represent exponential growth or exponential decay? 8.7 Exponential Growth and Decay

This function represents exponential decay. 8.7 Exponential Growth and Decay

C = $25,000 T = 12 R = 0.12 Growth factor = 1.12 Your business had a profit of $25,000 in If the profit increased by 12% each year, what would your expected profit be in the year 2010? Identify C, t, r, and the growth factor. Write down the equation you would use and solve. 8.7 Exponential Growth and Decay

Iodine-131 is a radioactive isotope used in medicine. Its half-life or decay rate of 50% is 8 days. If a patient is given 25mg of iodine-131, how much would be left after 32 days or 4 half-lives. Identify C, t, r, and the decay factor. Write down the equation you would use and solve. 8.7 Exponential Growth and Decay C = 25 mg T = 4 R = 0.5 Decay factor = 0.5