Name: 8 th Math Points / What number is 100 times larger than 0.4? (1 pt) 2. What does 4³ mean? (1 pt)

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1 Name: 8 th Math Points /20 Growing, Growing, Growing Assessment Answer each question, making sure to show your work or provide an explanation or sketch to support your answer in the box. Circle final answer. 1. What number is 100 times larger than 0.4? (1 pt) 2. What does 4³ mean? (1 pt) 3. What number is 1,000 times smaller than 80? (1 pt) 4. What is 9³? (1 pt) Page1

2 5. s ambition is to compete in a national bike race when he graduates high school, but he will need to purchase a new racing bike by then. After a lot of research, he finds a bike that suits him. The bike costs $1,500. Over the summer, Kai raises $1,000 by doing odd jobs and collecting contributions from his family and friends. He invests the money in an account that pays 8% interest per year on the balance in the account. A. 1. s account to be worth $1,500. (1 pt) Amount Year saved 0 $1, What is the growth factor? (1 pt) Page2

3 C. Graph the data sets in parts (A) and (B) on the grid below. Label each graph. (1 pt) 6. a. Fill in the table below for the given equations. (1 pt) x y Explain how you filled in the table Page3

7. The tables below represent three savings plans. (3 pts) Cela receives $20 for her birthday on January 1, puts it in her drawer, and adds $4 to it every month.

4 7. The tables below represent three savings plans. (3 pts) Cela receives $20 for her birthday on January 1, puts it in her drawer, and adds $4 to it every month. Beginning in January, Larry hides $20 under his mattress every month. Noah deposits $20 in a savings account at the beginning of January and makes no more deposits. The bank adds interest to his account at a rate of 1.2% per month. a. Whose plan is plan 1? Write an equation to model the growth in plan 1. b. Whose plan is plan 2? Write an equation to model the growth in plan 2. Page4

5 c. Whose plan is plan 3? Write an equation to model the growth in plan The table below shows an exponential pattern. (2 pts) a. Continue the table by giving the values for the next column. b. Write an equation that represents the pattern in the table. Page5

6 Study the pattern in the table. Tell whether the relationship between x and y is linear, exponential, or neither, and explain your answer. If the relationship is linear or exponential, write an equation for it. (2 pts) 9. x y x y ,000 Page6

7 11. Decide whether each of the following statements is true or false. Explain your reasoning. (2 pts) a. b. Multiple Choice: Circle the answer that answers the question. (3 pts) 12. Which of these is another way to write 2 6? a c b. 2 6 d Page7

8 13. What is the equivalent to? a. b. c. d. 14. a. b. c. d. Page8

9 G rowing, G rowing, G rowing Test Answer Section SH O R T A NSW E R 1. ANS: A. 1. Amount Year saved 0 $1, , , , , , , Answers will vary. One possible answer: Take the amount saved and multiply by 1.08 and continue for each year B. 1. Year Bike Cost 0 $1, , , , , , , Answers will vary. One possible solution: Take the cost and multiply by 1.04 and continue for each year. Page9

10 3. 4% C. D increase. The graph shows that the difference between the two amounts E. avings is increasing with a greater growth factor than the cost of the bike, so he will eventually have enough money saved to purchase it. After 11 be $2, PTS: 1 DIF: L2 REF: Growing Growing Growing Partner Quiz OBJ: Investigation 3: Growth Factors and Growth Rates NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 3.2 Growth Rates KEY: compound growth growth rate growth factor 2. ANS: a. x y Page10

11 x y ,875 b. The y value in grows at a faster rate. The numbers in the tables begin at the same value (15) but later corresponding x values are greater for thus this equation has a greater rate of growth. PTS: 1 DIF: L2 REF: Growing Growing Growing Question Bank OBJ: Investigation 3: Growth Factors and Growth Rates NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 3.2 Growth Rates KEY: table substitution 3. ANS: a. Larry's b. 1 month c. A = m, and d. Noah's Page11

12 e. 59 months f. g. Cela's h. 5 months i. A = m PTS: 1 DIF: L2 REF: Growing Growing Growing Question Bank OBJ: Investigation 1: Exponential Growth NAT: NAEP G3d TOP: Problem 1.4 Comparing Growth Patterns KEY: writing equations table 4. ANS: a. x = 5, y = 7776 b. c. The growth factor is 6. It can be found by dividing any y value by the previous y value. PTS: 1 DIF: L2 REF: Growing Growing Growing Question Bank OBJ: Investigation 3: Growth Factors and Growth Rates NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 3.3 Connecting Growth Rates and Growth Factor KEY: exponential pattern table writing equations growth factor 5. ANS: a. 20 gal 2.5 gal/min = 8 min b. The relationship is linear: w = 2.5t, where w is the water the bathtub will hold and t is the time in minutes to fill it. PTS: 1 DIF: L2 Page12

13 REF: Growing Growing Growing Additional Practice Investigation 2 OBJ: Investigation 2: Examining Growth Patterns NAT: NAEP G3d TOP: Problem 2.1 y-intercepts other than 1 KEY: growth rate linear equations exponential pattern writing equations 6. ANS: linear, PTS: 1 DIF: L2 REF: Growing Growing Growing Additional Practice Investigation 2 OBJ: Investigation 2: Examining Growth Patterns NAT: NAEP G3d TOP: Problem 2.1 y-intercepts other than 1 KEY: linear equations exponential pattern writing equations 7. ANS: exponential; PTS: 1 DIF: L2 REF: Growing Growing Growing Additional Practice Investigation 2 OBJ: Investigation 2: Examining Growth Patterns NAT: NAEP G3d TOP: Problem 2.1 y-intercepts other than 1 KEY: linear equations exponential pattern writing equations 8. ANS: a. about $1791 b. The relationship is exponential: V = 1000(1.06 y ), where V is the value and y is the number of years. PTS: 1 DIF: L2 REF: Growing Growing Growing Additional Practice Investigation 3 OBJ: Investigation 3: Growth Factors and Growth Rates NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 3.2 Growth Rates KEY: interest linear equations exponential pattern writing equations Page13

14 9. ANS: a. False, since and. b. False, since or PTS: 1 DIF: L2 REF: Growing Growing Growing Additional Practice Investigation 5 OBJ: Investigation 5: Patterns with Exponents NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 5.2 Operating with Exponents KEY: simplify expressions exponents 10. ANS: a. False, b. False, c. True, d. False, e. True, any base with an exponent of zero equals one. PTS: 1 DIF: L2 REF: Growing Growing Growing Unit Test OBJ: Investigation 5: Patterns with Exponents TOP: Problem 5.3 Exploring Exponential Equations KEY: simplify expressions exponents M U L T IPL E C H O I C E 11. ANS: A PTS: 1 DIF: L2 REF: Growing Growing Growing Multiple Choice OBJ: Investigation 1: Exponential Growth TOP: Problem 1.2 Representing Exponential Relationships form standard form NAT: NAEP G3d KEY: exponential 12. ANS: B PTS: 1 DIF: L2 REF: Growing Growing Growing Multiple Choice OBJ: Investigation 5: Patterns with Exponents NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 5.2 Operating with Exponents KEY: simplify expressions Page14

15 13. ANS: D PTS: 1 DIF: L2 REF: Growing Growing Growing Multiple Choice OBJ: Investigation 5: Patterns with Exponents NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 5.2 Operating with Exponents KEY: exponents simplify expressions 14. ANS: D PTS: 1 DIF: L1 REF: Growing Growing Growing Skills Practice Investigation 5 OBJ: Investigation 5: Patterns with Exponents NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g TOP: Problem 5.2 Operating with Exponents KEY: exponent base multiplying powers Page15

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