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Now-Next Basics Now-Next Rules are recursive rules that explain how to get from one number in a sequence to the next. In order to set up a Now-Next rule you need to know two things: Your starting value How your values are changing NEXT = NOW ± # NEXT = NOW × # NEXT = NOW ÷ #

Write a Now Next rule that describes how to get from one number to the next in each sequence. 1,3,5,7,9,11…. Starts with 1 Next = Now + 2 2,4,8,16,32,64…. Starts with 2 Next = Now x 2

Write a Now-Next rule that describes how to get from one number to the next in each sequence. Be sure to state what number to start at. 1.1, 0, -1, -2, -3, -4, -5… 1.1, 3, 9, 27, 81… 1.-2, 1, 4, 7, 10, 13… 1.Starts with 1 ; Next = Now Starts with 1; Next = Now x 3 3.Starts with - 2; Next = Now +3

Now-Next Equations and Tables Number of Weeks Savings Account Balance 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 0100 Complete the table. After 0 weeks, you would have $100 in the account because that is your starting value.

Now-Next Equations and Tables Number of Weeks Savings Account Balance 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. And the start value is $100

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. As with Now-Next Rules, we need to have the first value in the sequence or the starting point in a particular situation or word problem. Now we need to figure out how our values will be changing. 150 pieces to start with Since you are eating the M&M’s there will be a decrease of 7 every 5 minutes. Next = Now – 7 Now-Start = 150

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. How many M&M’s will be left after 30 minutes? Time - minutes M&M’s Time - minutes M&M’s

In the book ​ Alice’s Adventures in Wonderland ​, by Lewis Carroll, Alice grows when she eats a piece of cake. If her original height is 4ft 6in and her height doubles every time she takes one bite of cake, how tall will she be after 5 bites of cake? Write a NOW NEXT rule that describes her growth. Height (feet) 4ft 6in 9 ft 18 ft 36 ft 72 ft 144 ft

The population of North Carolina in 2012 was 9,752,073 with an annual population change of about 1%. If this growth rate continues, what will be the population in North Carolina in 2020? Write an NOW NEXT rule that describes the population growth. Ways to write the Now-Next Equation: Next = 0.01∙Now + Now Next = 1.01 ∙ Now Starting At: 9,752,073

A local pond is having a problem with its fish population. So many people have been fishing in this pond that a wildlife specialist says that the fish population has declined 2% each year for the past several years. a). Write a NOW-NEXT rule that can be used to find the next year’s fish population. b). If the current population of the fish is estimated to be about 1000, how many fish will be in the pond five years from now if this rate of decrease continues?

John gets an allowance of $15 a week from his parents. He is trying to save money to buy a new cell phone. The phone that John wants is $199. a). How much money will he have in five weeks? b). If John saves all of his money, how long will it take him to save up enough money to buy a new cell phone? c). Write a NOW-NEXT rule to show the relationship between the amount of money John has this week and the amount that he will have next week.

Writing Equations Let’s say you are looking for the weekly balance (y) in a savings account if you deposit $20 per week (x) and your initial balance is $100. Write an equation for the weekly balance in terms of the number of weeks. Next = Now + 20, SA 100 y = x

Writing Equations Alice grows when she eats a piece of cake. If her original height is 4ft 6in and her height doubles every time she takes one bite of cake, how tall will she be after 5 bites of cake? Next = (Now) (2), SA: 4.5

Practice! 1. 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. 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) Write an equation that models the word problem. 1a. Next = Now – 176, SA: 11,000 SecondsFeet from ground 011, , , , ….. 99, ,240 1c. y = 11,000 – 176x

2. The population of Cadillac, MI, is decreasing at a rate of 5% per year. a) Write a Now-Next equation that models the population of Cadillac, MI, if the population now is 10,280. b) Make a table for the first 5 years. c) Write an equation that models the word problem.

#2 Answers 2a. Next = Now * (0.95) SA: b. SecondsFeet from ground 010,280 19,766 29, , , ,954.5 y = (10,280)(0.95) x