Writing Exponential Equations Day 2

Size: px

Start display at page:

Download "Writing Exponential Equations Day 2"

Ambrose Copeland
6 years ago
Views:

1 Writing Exponential Equations Day 2 MGSE9 12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions (integer inputs only). MGSE9 12.A.CED.2 Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase in two or more variables refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.) Feb 28 10:54 AM 1

2 What am I learning today? How to write the equation for an exponential function How will I show that I learned it? Recognize an exponential scenario and write an equation to model it Aug 18 1:21 PM 2

3 Complete the Paper Folding Task How many times do you think a football size piece of paper could be folded? Oct 29 12:55 PM 3

4 An exponential function is created by MULTIPLYING BY THE SAME NUMBER. It takes the general form of f(x) = a(b) x + k where a is the initial value, b is the multiplier, x is the number of times it's changed, and k is a constant. Oct 29 12:58 PM 4

5 Steps for writing exponential equations: Step 1: Find the value you are starting with. Label this "a". Step 2: Find your ratio of increase. If it is a %, change it to a decimal and add it to 1 if the problem is increasing or subtract it from 1 for decreasing. Label this "b". Step 3: Plug into the formula y = A(B) x Step 4: When solving, pay attention to the rate of increase. Divide your time by your rate to find the proper value of x. Oct 29 1:02 PM 5

6 Ex. A There are 25 bacteria in a sample. The bacteria triple every hour. a) Write an equation for this if x=# of hours. b) How many bacteria will there be in 4 hours? Oct 29 1:06 PM 6

7 Ex. B There are 10 mushrooms in your yard. The mushrooms double every 2 days. a) Write an equation for this if x=# of days. b) How many mushrooms will there be in 6 days? Oct 29 1:04 PM 7

8 Ex. C A hand sanitizer kills 1/2 of the germs after each use. You have 5,000,000 germs on your hands now. a) Write an equation for this if x=# of uses. b) How many germs will you have after 2 uses? c) How many germs will you have after 4 uses? Oct 29 1:04 PM 8

9 Sometimes, the change isn't a basic integer or fraction... Introduction: Your grandmother wants to help you save for college. She gave you $1 when you were 5. She promises to give you 20% more every year. How much money will she give you when you are 18? How much money will you have? Aug 22 3:44 PM 9

10 If there is a % change, the base is (1 + r) for growth and (1 - r) for decay. What's going to be the base of your exponential in the following cases? 1. 20% increase 2. 15% decrease 3. 8% increase 4. 4% decrease % increase % decrease Oct 29 1:08 PM 10

11 Ex. A The population of Atlanta was 420,000 in 2010 and expected to grow at a rate of 8% per decade. Predict the population, to the nearest ten thousand, for the year Aug 22 3:59 PM 11

12 Ex. B Caffeine is eliminated from the bloodstream at a rate of 25% per hour. There are initially 500 mg of caffeine. Predict the amount of caffeine in the bloodstream after 1 hour and 4 hours. Aug 22 3:59 PM 12

13 Ex. C Bill Gates put $ in a charity. This endowment pays out 6% of its money every year. How much money will be left in the account in 12 years? How much money will the charity pay out the 13th year? Aug 22 3:59 PM 13

14 Oct 29 1:14 PM 14

Name: How Long Does It Take? (Part 1)

Name: How Long Does It Take? (Part 1) Standards Addressed in this Task MGSE9-12.N.RN.1, MGSE9-12.N.RN.2, MGSE9-12.N.RN.3 Before sending astronauts to investigate the new planet of Exponentia, NASA decided