Now-Next Equations

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

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

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

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. After 0 weeks, you would have $100 in the account because that is your starting value.

Now-Next Equations and Tables After 1 week you would have an additional $20 in the account. What would your new balance be?

Now-Next Equations and Tables After 1 week you would have an additional $20 in the account. What would your new balance be? The new balance would be $120!

Now-Next Equations and Tables Complete the table.

Now-Next Equations and Tables 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.

Now-Next Equations and Tables 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.

Now-Next Equations and Tables 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.

Now-Next Equations and Tables So the correct Now-Next equation used to model this problem would be: Next = Now + 20 Now Start = 100

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.

Now-Next Equations First, let’s find the initial value. 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. 150 pieces of candy There are 150 pieces of candy in each bag so that would be the initial value.

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.

Now-Next Equations Important Information Initial Value - 150 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

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.

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.

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

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

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.

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.

Follow Up Questions Answer the following questions on loose leaf and hand them in to your teacher.

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)

Now-Next Equations