Name: ___________________________________________ Date_____________ Period: ____ Recursive Formulas from Word Problems Problem 1: Sally started a new job. After depositing her 1st paycheck into her bank account she had $225. Every week she was paid the same amount. After her 8th paycheck she had $1275 in her bank account. a) Complete the table Week
1
2
3
4
5
6
7
8
$
b) How much was she paid every week? Explain how you found this. _______________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ c) Create a graph of this situation. d) Write the recursive formula for this situation. ____________________________________________ y
1275
1200
1125
1050
975
____________________________________________ 900
e) Explain what the recursive formula means in the context of Sally’s account.
____________________________________________ 750
____________________________________________ f) How much did Sally have in her bank account when she started working? ____________________________________________ 825
675
600
525
450
375
300
225
150
75
1
2
3
4
5
6
7
8
9
____________________________________________ !
Recursive Formulas: Recursive Formulas from Word Problems 1 10
x
Name: ___________________________________________ Date_____________ Period: ____ Problem 2) Johnny bought his first car. After 1 year he was upset because Kelly Blue book said his car was only worth $17,000. His parents told him that each year his car will depreciate (decrease in value) 10%. How much will his car be worth after 8 years? a) Complete the table Year
1
2
3
4
5
6
7
8
$
y
17000
16000
b) Create a graph for this situation. c) Write the recursive formula for this situation. _________________________________________ _________________________________________ 15000
14000
13000
12000
11000
10000
9000
d) Explain what the recursive formula means in the context of Johnny’s car value.
_________________________________________ 8000
7000
6000
5000
4000
_________________________________________ e) How much did Johnny originally pay for the car? _________________________________________ 3000
2000
1000
1
2
3
4
5
6
7
8
9
10
11
x
_________________________________________ Problem 3: 1. What function family did Problem 1 belong to? Explain. __________________________________________________________________________________ 2. What function family did Problem 2 belong to? Explain. __________________________________________________________________________________ !
Recursive Formulas: Recursive Formulas from Word Problems 2 Name: ___________________________________________ Date_____________ Period: ____ Teacher Directions Materials: Calculator – 1 per student Copies of activity sheet – 1 per student Objective: Students will have to interpret word problems and write the recursive formula that
defines it. Directions: Problem 1: Students should work in pairs. Students will spend most of their time on “a) Complete the table”. Let students struggle with this. Look for interesting ways students found to complete the table. Have students share how they completed the table. •
•
•
Students may have guessed until they found the common difference that worked. Students may have found the difference between the 1st and 8th term and divided. Students may have used the slope formula. Note: Before moving on, call on students to share their answers to each question. Problem 2 & 3: Have students work on this problem and intervene only when needed. Possible problems will be how to depreciate a value by 10%. A discussion about depreciation and how to take 10% of a number will help. Suggestion: it may be helpful to consider what 90% of the value is instead. Call on students to share their results then pass out ticket out the door. !
Recursive Formulas: Recursive Formulas from Word Problems 3