1. Wednesday, February 12, 2014 SWBAT apply exponential decay to solve real-world problems.

2. Do Now Learning Target: SWBAT apply exponential decay to solve real-world problems. Homework: Study for COMMON ASSESSMENT tomorrow! 2/10/14 Learning Target: Homework: 1)Steven put $500 into a Chase bank savings account with a 2% interest rate compounded yearly. a)Write a function expressing the amount of money in the account after t years. b)How much money will be in the account after 50 years? c)(Challenge) If Steven put another $500 into the account after 25 years, how much money would he have after 50 years?

3. Do Now Answers 1)Steven put $500 into a Chase bank savings account with a 2% interest rate compounded yearly. a)Write a function expressing the amount of money in the account after t years. b)How much money will be in the account after 50 years? c)(Challenge) If Steven put another $500 into the account after 25 years, how much money would he have after 50 years?

4. Composition book rules and grading First page – Write “Table of Contents” at the top Table of Contents 1 Date Day: Learning Target Summary Page # 02/10/14 Mon: Exponential Functions Intro 5 02/11/14 Tues: Simple Interest 6 02/12/14 Tues: Exponential Decay 8

5. Common Assessment #5

6. Penny Flipping! Say you have 100 pennies. You flip them. How many come up heads? ______ You set aside all the pennies that came up tails. You flip the rest. How many pennies come up heads?______ 50 25 12-13 6 3 2 1

7. Unfortunately, we don’t have 100 pennies… But we can use calculators to simulate the penny flipping! Calculator can generate a Random Integer between 0 and 1 (so, either 0 or 1) 50% chance of number being 0, and 50% chance of it being 1

8. Here’s how! [MATH] > [PROB] > randInt Let’s say….. 1 = heads; 0 = tails How about 100 coins?... 1)How do we know how many heads came up? 2)Is there a way that we can use the calculator to help us calculate it?

9. Is there a way that we can use the calculator to help us calculate the # of heads? [2 nd ] [LIST] > [MATH] > sum [2 nd ] [LIST] > [MATH] > sum I claim 51 of the 100 coins came up heads. Why?

10. You’re ready… Let’s do this experiment! Complete the following chart and answer the following questions 1)What is happening to the # of heads after each experiment? 2) What percentage are you decreasing the # of heads with each experiment? 3)Come up with a function that relates # of heads with experiment #. Decreasing exponentially ~50%

11. 1)What is happening to the # of heads after each experiment? 2) What percentage are you decreasing the # of heads with each experiment? 3)Come up with a function that relates # of heads with experiment #. Decreasing exponentially ~50% 1)How many heads would you expect for the 4 th experiment? 2)What if the coin were rigged, and the tails side showed up 75% of the time. Write a new function that relates # of heads with experiment #. Hint: What is the percent decrease of heads after each experiment? 75%

12. Independent Practice Complete the classwork portion of your worksheet Questions #1-4, Challenge Dog Scenario is on the back

13. 1.A city population, which was initially 15,500, has been dropping 3% a year. a) Write an exponential function that represents the city population (A(t)) as a function of how much time (t) has passed. b) What is the city’s population after 20 years? 2.The value of a $3000 computer decreases about 30% each year.. a) Write an exponential function for the computer’s value after t years. b) How much is the computer worth after 4 years? a)b)b) b)b)

14. 3. The number of acres of Ponderosa pine forests decreased in the western United States from 1963 to 2002 by 0.5% annually. In 1963 there were about 41 million acres of Ponderosa pine forests. a) Write a function that models the number of acres of Ponderosa pine forests in the western United States over time. b) To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002? a)b)b)

15. 4.Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each round, half of the players are eliminated. a) Write a function that models the number of participants with each passing round. b) How many players remain after 5 rounds? a)b)b)

16. Exit Ticket Turn into the tray when you are done Also turn in HW from yesterday

17. Closing Don’t forget Common Assessment is TOMORROW!