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Now-Next Equations Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.

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Now-Next Basics Now-Next equations are recursive equations that use a previous value (or answer) to get to the next value. Your equations will always start out as Next = Now (and then you include how it changes) There will NEVER be variables in a Now-Next equation

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Now-Next Basics In order to set up a Now-Next equation you need to know two things: Your starting value How your values are changing

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**Now-Next Equations and Tables**

Let’s say you are looking for the weekly balance in a savings account if you deposit $20 per week and your initial balance is $100. Number of Weeks Savings Account Balance After 0 weeks, you would have $100 in the account because that is your starting value.

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**Now-Next Equations and Tables**

Let’s say you are looking for the weekly balance in a savings account if you deposit $20 per week and your initial balance is $100. Number of Weeks Savings Account Balance 100 After 0 weeks, you would have $100 in the account because that is your starting value.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 After 1 week you would have an additional $20 in the account. What would your new balance be?

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 After 1 week you would have an additional $20 in the account. What would your new balance be? The new balance would be $120!

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 Complete the table.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 2 140 Complete the table.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 2 140 3 160 Complete the table.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 2 140 3 160 4 180 Complete the table.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 2 140 3 160 4 180 Now that we have the table, we can use it to write our Now-Next equation. We need to think about how our balance changes for every increase of 1 in the number of weeks.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 2 140 3 160 4 180 We can see from the table or from our initial problem that it increases (adds) $20 each week. So our equation would be Next = Now + 20 because we are adding $20 to the current balance.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 2 140 3 160 4 180 But you’re not finished yet! What is missing? You need to have a starting value (or Now-Start) for every Now-Next equation. What would the Now-Start be for this problem? The Now-Start is 100 because it is the initial balance.

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**Now-Next Equations and Tables**

Number of Weeks Savings Account Balance 100 1 120 2 140 3 160 4 180 So the correct Now-Next equation used to model this problem would be: Next = Now + 20 Now Start = 100

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**Let’s pick out the important information first.**

Now-Next Equations Now let’s try to make our Now-Next equation without using a table. Take a look at this problem. In each large bag of M&M’s, there are about 150 pieces of candy. Suppose you eat 7 M&M’s every 5 minutes. Write a Now-Next equation to model the number of M&M’s left. Let’s pick out the important information first.

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**First, let’s find the initial value.**

Now-Next Equations First, let’s find the initial value. 150 pieces of candy In each large bag of M&M’s, there are about 150 pieces of candy. Suppose you eat 7 M&M’s every 5 minutes. Write a Now-Next equation to model the number of M&M’s left. There are 150 pieces of candy in each bag so that would be the initial value.

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**Now we need to figure out how our values will be changing.**

Now-Next Equations Now we need to figure out how our values will be changing. In each large bag of M&M’s, there are about 150 pieces of candy. Suppose you eat 7 M&M’s every 5 minutes. Write a Now-Next equation to model the number of M&M’s left. you eat 7 M&M’s every 5 minutes Since you are eating the M&M’s there will be a decrease of 7 every 5 minutes.

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**Now-Next Equations Next = Now – 7 Important Information**

Initial Value M&M’s Change - Decrease of 7 every 5 minutes Now we can make our Now-Next equation. Remember that your equation will always start out as Next = Now… Find the Now-Next equation. Next = Now – 7 Now-Start = 150

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**Now-Next Equations Next = Now – 7 Now-Start = 150**

Once we have our Now-Next equation, we can use the calculator to help build a table of values. Your first step will always be to enter your initial value then hit ENTER.

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**Now-Next Equations Next = Now – 7 Now-Start = 150**

Next, you’ll need to enter your Now-Next equation to get your list of values. Instead of using the word “Now”, the calculator uses the last answer function.

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**To do this, you’ll hit the 2nd Key then the Negative Sign.**

Now-Next Equations Next = Now – 7 Now-Start = 150 To do this, you’ll hit the 2nd Key then the Negative Sign.

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**Write the rest of your equation as you normally would then hit ENTER.**

Now-Next Equations Next = Now – 7 Now-Start = 150 Write the rest of your equation as you normally would then hit ENTER.

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**Now-Next Equations Next = Now – 7 Now-Start = 150**

You can continue to hit ENTER to get the next values. Remember, hitting the ENTER button represents a 5 minute interval.

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**Number of 5 Minute Intervals**

Now-Next Equations Next = Now – 7 Now-Start = 150 We can now use these values to make a table. We can now use these values to make a table. Time Interval 0 minutes 5 minutes 10 minutes 15 minutes 20 minutes Number of 5 Minute Intervals 1 2 3 4 Number of M&M’s Left 150 143 136 129 122

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**Follow Up Questions Answer the following questions on loose leaf**

and hand them in to your teacher.

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Follow Up Questions In a free fall dive, a person will travel 176 feet every second. A safe jumping height is from a plane that is 11,000 feet above the ground. Write a Now-Next equation that models the distance of the jumper from the ground. Make a table for the first 10 seconds of free fall. A skydiver is supposed to pull the cord when they are 4,000 feet from the ground. To the nearest second, when should a skydiver pull their cord? (Remember you should pull your cord as close as possible to 4,000 feet, but it would be safer to pull it earlier than later) Explain how you used your calculator to get your answers for questions (b) and (c)

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