Name: ______Date: ______Block: ______

Study Guide Growing, Growing, Growing Inv 3 QUIZ

Kai’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 $1,050. 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 4% interest per year on the balance in the account.

A.1.Complete the table below to the amount in Kai’s savings account after 6 years.

Year / 0 / 1 / 2 / 3 / 4 / 5 / 6
Amount Saved / $1,000 / $1081.60 / $1125.86 / $1169.85 / $1169.85 / $1216.65 / $1265.32

Explain how you completed the table by showing your work for the first two years. $1000 x 1.04 = $1040 then $1040 x 1.04 = S1081.61

3.What is the growth factor? 1.04

4. Write an equation that Kai could use to figure out how much money he has saved over the years.

Initial Value: 1000Growth Factor: 1.04

Hint  Equation:

B.1.Suppose that the cost of the bike rises by 2% per year. Complete the table below to show how the cost increases. There is no sales tax where Kai lives.

Year / 0 / 1 / 2 / 3 / 4 / 5 / 6
Bike Cost / $1, 050 / $1071 / $1092.42 / $1114.27 / $1136.55 / $1159.28 / $1182.47

Explain how you completed the table by showing your work for the first two years. $1050 x 1.02=$ 1071 and $1071 x 1.02=1092.42

3.What is the growth rate? 2%

4. Write an equation that Kai could use to figure out how much the bike would be over the years.

Initial Value: $1050Growth Factor: 1.02

Hint  Equation:

  1. Graph the data sets in parts (A) and (B) on a separate sheet of paper. Graph BOTH tables onto one graph. Label each with a different color for the savings and the cost of the bike.

D.Look at your tables and graphs.

1.) Which one starts out higher on the graph paper? (CIRCLE ONE) Blue or Red

Why? The initial value is higher.

2.) Which one is growing faster by looking at the graph? (CIRCLE ONE) Blue or Red Why? The line is a steeper line on the graph.

3.) Which one is growing faster by looking at the growth factor? (CIRCLE ONE) Blue or Red

Why? The growth rate is higher

E.Will Kai ever be able to buy the bike? (Hint: Continue the tables or the graphs to look at the future amounts. Do they or will they ever cross?) CIRCLE ONE YES OR NO

Why? Because her saved money in Blue will be over the price of the bike at year 3.

Tribetts are fuzzy insects that reproduce at the rate of 40% every day. Suppose you begin with 200 tribetts.

a.Make a table showing the growth in the number of tribetts for the first 10 days.

Days / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
# of Tribetts / 200 / 280 / 392 / 548 / 768 / 1075 / 1505 / 2108 / 2951 / 4132 / 5785

b.On what day will there first be 1000 tribetts? Day 5

  1. Write an equation for the relationship between days d and numbers of tribettsT.

Initial Value: 200Growth Factor: 1.4

Hint  Equation:

RULE: Growth factor = growth rate (as a decimal) + 1

Growth rate= growth factor – 1 x 100