Writing Exponential Equations Day 2

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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 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 3

4 Parameter: a term in a function that determines a specific form of a function but not the nature of the function. The numbers that give a function its shape. For an exponential function: a, b and k are the usual parameters (initial value, base, and constant). Changing the parameters changes the function and the graph. Sep 20 9:39 PM 4

5 For the following, indicate the parameters. 1. f(x) = 4(0.8) x 2. g(x) = 2(4) x h(x) = 2/3(1+.08) x 3 4. j(x) = 4(1.6) x/5 Nov 1 1:00 PM 5

6 Steps for Writing Exponential Equations from a Table: Step 1: Find the y-intercept. Label this "a". Step 2: Find your ratio of change by dividing the 2nd # by the 1st #. Check it by dividing the 3rd # by the 2nd #. Label this "b". Step 3: Plug into the formula y = A(B) x Oct 29 1:02 PM 6

7 Returning to a past example... Introduction: Your grandmother wants to help you save for college. She gave you $100 when you were 5. She promises to give you 30% 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 7

8 How can you tell by looking at the table if you have an exponential growth or decay function? Oct 29 1:08 PM 8

9 Your credit card debt is growing according to the following table. Month Debt 0 $ $ $ $ $58.49 Write an equation to represent how much you owe based on how many months you haven't paid off the debt. Nov 1 1:19 PM 9

10 Your credit card debt is growing according to the following table. Month Debt 0 $ $ $ $ $58.49 If you wait 1 year to pay off the debt, how much will you owe? How much additional money are you paying in interest? Nov 1 1:19 PM 10

11 Your credit card debt is growing according to the following table. Month Debt 0 $ $ $ $ $58.49 When is your debt growing more quickly? Between months 1 and 3 or months 10 and 12? Nov 1 1:19 PM 11

12 The table below represents the number of mosquitos based on the number of times a farmer has used a pesticide. # of uses # of mosquitos Write an equation to represent how many mosquitos there are based on how many times the pesticide has been used. Nov 1 1:27 PM 12

13 The table below represents the number of mosquitos based on the number of times a farmer has used a pesticide. # of uses # of mosquitos If the farmer uses the pesiticide 10 times, how many mosquitos would he expect to be left? Nov 1 1:27 PM 13

14 The table below represents the number of mosquitos based on the number of times a farmer has used a pesticide. # of uses # of mosquitos When are the mosquitos dying more quickly? Between uses 0 and 2 or uses 4 and 6? Nov 1 1:27 PM 14

15 Interest Growth A = final amount of money P = Principal Investment (initial amount of money) r = rate of change n = number of times compounded per year t = number of years Nov 1 1:33 PM 15

16 If you have $5000 compounded quarterly at a rate of 6%, how much will you have after 5 years? If you have $5000 compounded monthly at a rate of 6%, how much will you have after 5 years? If you have $5000 compounded monthly at a rate of 8%, how much will you have after 5 years? If you have $5000 compounded monthly at a rate of 8%, how much will you have after 10 years? Nov 1 1:41 PM 16

17 Nov 4 9:47 AM 17

Writing Exponential Equations Day 2

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,