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

2. 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

3. 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

4. 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.

5. 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.

6. 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?

7. 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!

8. Now-Next Equations and Tables
Number of Weeks
Savings Account Balance
100 1
120
Complete the table.

9. Now-Next Equations and Tables
Number of Weeks
Savings Account Balance
100 1
120 2
140
Complete the table.

10. Now-Next Equations and Tables
Number of Weeks
Savings Account Balance
100 1
120 2
140 3
160
Complete the table.

11. Now-Next Equations and Tables
Number of Weeks
Savings Account Balance
100 1
120 2
140 3
160 4
180
Complete the table.

12. 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.

13. 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.

14. 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.

15. 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

16. 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.

17. 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.

18. 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.

19. 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

20. 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.

21. 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.

22. 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.

23. 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.

24. 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.

25. 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

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

27. 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)