Exponents Nov 1-10:06 AM Table Of Contents Section 1: Zero and Integer Exponents Section 2: Section 3: Multiplication Properties of Exponents Section 4: Division Properties of Exponents Section 5: Geometric Sequences Section 6: Section 7: Exponential Growth and Compound Interest Section 8: Exponential Decay and Half Life Nov 1-6:44 PM Section 1: Zero and Integer Exponents Objective: Nov 1-10:07 AM 1
Look at the following examples of powers: exponents. Nov 1-10:08 AM What did you determine? Nov 1-10:55 AM A botanist has taken over a study of a plant whose height doubles every day. On the fourth day after the experiment began, the plant was 16 inches tall. Nov 1-10:13 AM 2
Complete the table: What is the pattern of the Value row going from 5 up to Nov 1-10:20 AM Zero Exponents Negative Exponents Algebraic Definitions One cup is 2 Nov 1-6:08 PM 3
m. Nov 1-6:08 PM Nov 1-6:09 PM Nov 1-6:11 PM 4
Nov 1-6:11 PM Nov 1-6:12 PM Base Expanded Form: In ( 3), the base is negative because the negative sign is inside the parentheses. In the base (3) is positive. Nov 1-6:13 PM 5
Nov 1-6:17 PM Nov 1-6:19 PM Nov 1-6:20 PM 6
Nov 1-6:20 PM Evaluate the expression for the given value of the variables. for Nov 1-6:22 PM Evaluate the expression for the given values of the variables. 2 Nov 1-6:23 PM 7
Evaluate the expression for the given value of the variable. for Nov 1-6:25 PM Nov 1-6:25 PM Simplify Fully: Nov 1-6:26 PM 8
Simplify Fully: Nov 1-6:26 PM Simplify Fully: Nov 1-6:26 PM Nov 1-6:30 PM 9
Nov 1-6:31 PM Nov 1-6:33 PM Section 2: Powers of 10 and Scientific Notation Objective: Evaluate and multiply by Nov 1-6:40 PM 10
Powers of Ten 1/10 1/100 1/1000 Nov 1-6:50 PM Powers of Ten 1/10 1/100 1/1000 Nov 1-6:50 PM Powers of 10 Nov 1-7:03 PM 11
Nov 1-7:06 PM Nov 2-10:15 AM If you do not see a decimal point in a number, Nov 2-10:16 AM 12
Nov 2-10:17 AM Nov 2-10:18 AM Multiplying by Powers of 10 Nov 2-10:19 AM 13
Find the value of the expression: Nov 2-10:19 AM Find the value of the expression: Nov 2-10:19 AM Find the value of the expression. Nov 2-10:20 AM 14
Find the value of the expression. Nov 2-10:22 AM Scientific notation 10 9.98 10 Nov 2-10:23 AM written not in scientific notation. b) Write Saturn's distance from the sun in Nov 2-2:37 PM 15
Jupiter has a diameter of approximately Nov 2-2:42 PM Write the value in Scientific Notation: Nov 3-12:25 PM Nov 2-2:43 PM 16
Ordering Numbers from Least to Greatest Nov 2-6:27 PM Find the value of the expression: Nov 2-7:18 PM Find the value of the expression: Nov 2-7:23 PM 17
Section 3: Multiplication Properties of Exponents Objective: Use multiplication properties of simplify expressions. Nov 2-7:25 PM Simplifying Exponential Expressions: Nov 2-7:32 PM Nov 2-7:52 PM 18
Is the expression fully simplified? Nov 4-10:42 AM Is the expression simplified fully? Nov 4-10:43 AM for multiplication of exponents! Nov 6-1:39 PM 19
Product of Powers Property In words...when you are Nov 4-10:41 AM Nov 4-10:44 AM Nov 4-10:46 AM 20
Nov 4-10:46 AM Step 1: Write each term in Scientific Notation Step 2: Calculate distance using: D = Click 1.5 10 What Algebraic Property is being used here? Nov 4-10:48 AM Step 2: Calculate distance using: D = 1.5 10 What Algebraic Property is being used here? ( 2.79 ) Solution: mi. Nov 4-10:48 AM 21
Nov 4-11:07 AM partner up with your neighbor Share...share your rule(s) Nov 6-1:18 PM Power of a Power Property = In words...when you are raising a power to a power, Nov 4-10:41 AM 22
Nov 4-11:08 AM Nov 4-11:09 AM Nov 4-11:10 AM 23
Nov 4-11:11 AM Nov 6-1:25 PM Power of a Product Property In words...when you are Nov 4-10:41 AM 24
Nov 6-1:29 PM Nov 6-1:32 PM Nov 6-1:33 PM 25
Nov 6-1:35 PM Section 4: Division Properties of Exponents Objective: Use division properties of simplify expressions. Nov 2-7:25 PM SUBTRACTION for division of exponents! Nov 6-1:39 PM 26
Nov 6-1:35 PM Quotient of Powers Property Nov 6-1:55 PM Nov 6-2:33 PM 27
Nov 6-2:34 PM Nov 6-2:34 PM ). Nov 6-2:38 PM 28
Nov 6-2:45 PM Expand: What do you notice about the relationship and denominator? Nov 6-2:47 PM Positive Power of a Quotient Property positive power, Nov 6-1:55 PM 29
Nov 6-2:52 PM Nov 6-2:53 PM Nov 6-2:55 PM 30
Nov 6-2:50 PM Negative Power of a Quotient Property a b a = b negative power, Nov 6-1:55 PM Nov 6-3:01 PM 31
Nov 6-3:01 PM The Republic of Botswana has an area of 6 x 10 kilometers. Its population is about 1.62 x 10 What is the population density of Botswana? (HINT: Nov 6-3:05 PM Section 5: Geometric Sequences Objective: Find the Nov 1-10:07 AM 32
Step 1: Find the common ratio,, by dividing each term by the one before it. = 3 Step 2: Use the common ratio and multiply to find the next 3 terms. Nov 7-6:34 PM What is the common ratio in the following geometric sequence? Nov 7-6:50 PM The next term in the following geometric False Nov 7-6:52 PM 33
Find the common ratio and the next term in the following geometric sequence: -80 80 F -20 Nov 7-6:55 PM Given the geometric sequence: Find the common ratio and write a function in the = 3 = 6 = 12 = 24 Nov 7-6:59 PM Find the Nov 14-4:02 PM 34
500 What is the 7th term of the sequence? Nov 14-4:40 PM Find the 6th term of the sequence? Nov 14-4:42 PM A ball is dropped from a tower. The table shows the heights of the balls bounces, which form a geometric Nov 14-4:43 PM 35
The table shows a car s value for three years after it is b) What is the common ratio, r? How much will the car be worth after 8 years? Nov 14-4:46 PM Nov 15-10:08 AM b = growth rate Nov 15-2:06 PM 36
) = 500(1.035) models the amount of How much money will there be in Nov 15-2:11 PM ) = 200,000(0.98) time in years, models the population of a city. Nov 15-2:12 PM ) = 200,000(0.98), models the population of a city. Nov 15-2:14 PM 37
) = 200,000(0.98), models the population of a city. 0.98 Nov 15-2:14 PM Determine if the table satisfies an exponential function: Do the x-values increase by a constant amount? Are the y-values multiplied by a constant Nov 15-2:16 PM Do the ordered pairs represent an exponential Nov 15-2:24 PM 38
Do the ordered pairs represent an exponential Nov 15-2:24 PM Do the ordered pairs represent an exponential Nov 15-2:24 PM To graph an exponential function: (positive, negative, and 0) Plot the points and connect them with a smooth Nov 15-2:29 PM 39
-2-1 0 1 2 Nov 15-2:31 PM Nov 15-2:31 PM x Nov 15-2:31 PM 40
x Nov 15-2:31 PM Nov 15-2:37 PM where a > 0 y = final amount a = original amount / initial starting value r = rate of growth / percentage written in decimal form Nov 15-2:40 PM 41
The original value of a painting is each year. Write an exponential growth 10 y = final amount a = original amount / initial starting value r = rate of growth / percentage written in decimal form Nov 15-3:17 PM A sculpture is increasing in value at a rate of 8% per year, and its value in 2000 was $1200. Write an exponential growth function to model this Nov 15-3:19 PM Find the value of the condo in 2015. Nov 16-9:52 AM 42
P where a > 0 P = original amount / initial starting value r = rate of growth / percentage written in decimal form t = time in years Nov 15-2:40 PM annually = 1 time per year biannually = 2 times per year quarterly = 4 times per year monthly = 12 times per year Nov 21-9:25 AM Write a compound interest function to model the invested at a rate of for years A = final amount P = original amount / initial starting value Nov 15-3:21 PM 43
Nov 16-10:07 AM Nov 16-10:14 AM Objective: Solve problems involving exponential Nov 15-2:37 PM 44
Exponential Decay ( 1 - y = final amount Nov 15-2:40 PM and the value function to model this situation. Then find the car's value y = final amount a = original amount / initial starting value r = rate of growth / percentage written in decimal form Nov 15-3:17 PM The honey bee population is decreasing at a rate of billion honey bees in 2011, how many will there be in 2020? Nov 20-3:07 PM 45
The value of a house is decreasing in value. The original value of the house was $350,000. It is decreasing at a rate of 4.5% per year. What is it's worth after 10 years? Choose the correct Nov 20-3:12 PM A half life function has the form: ( 0.5 ) y = final amount t = number of half lives that occur in the given time Nov 15-2:40 PM Find the number of half lives and the amount left from 8 32 5 F 0.1171875 g Nov 20-3:36 PM 46
1.953125 grams 19.53125 grams Nov 20-3:30 PM Nov 20-3:48 PM 47