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 TablesNumber of

WeeksSavings Account

BalanceLet’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.



Balance

0 100

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.



Balance

0 100After 1 week you would have an additional $20 in the account. What would your new balance be?



Balance

0 100

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!



Balance

0 100

1 120Complete the table.



Balance

0 100

1 120

2 140Complete the table.



Balance

0 100

1 120

2 140

3 160

Complete the table.



Balance

0 100

1 120

2 140

3 160

4 180

Complete the table.



Balance

0 100

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.



Balance

0 100

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 beNext = Now + 20

because we are adding $20 to the current balance.



Balance

0 100

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.



Balance

0 100

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

Now-Next EquationsNow 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.


There are 150 pieces of candy in each bag so that would be the initial

value.

150 pieces of candy

Now-Next Equations

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


Since you are eating the M&M’s there will be a decrease of 7 every 5

minutes.

you eat 7 M&M’s every 5 minutes

Now-Next EquationsImportant Information

Initial Value - 150 M&M’sChange - 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 – 7Now-Start = 150

Now-Next EquationsNext = 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-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-Start = 150

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

Sign.


Now-Start = 150

Write the rest of your equation as you

normally would then hit ENTER.


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-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 0 1 2 3 4

Number of M&M’s Left 150 143 136 129 122

Follow Up Questions

Answer the following questions on loose leafand hand them in to your teacher.

Follow Up QuestionsIn 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.

a) Write a Now-Next equation that models the distance of the jumper from the ground.

b) Make a table for the first 10 seconds of free fall.

c) 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)

d) Explain how you used your calculator to get your answers for questions (b) and (c)