# Lesson 1

Growing and Growing

### Problem 1

Which expression equals \(2^7\)?

\(2+2+2+2+2+2+2\)

\(2 \boldcdot 2 \boldcdot 2\boldcdot 2\boldcdot 2\boldcdot 2\boldcdot 2\)

\(2 \boldcdot 7\)

\(2+7\)

### Solution

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### Problem 2

Evaluate the expression \(3 \boldcdot 5^x\) when \(x\) is 2.

### Solution

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### Problem 3

The graph shows the yearly balance, in dollars, in an investment account.

- What is the initial balance in the account?
- Is the account growing by the same number of dollars each year? Explain how you know.
- A second investment account starts with $2,000 and grows by $150 each year. Sketch the values of this account on the graph.
- How does the growth of balances in the two account balances compare?

### Solution

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### Problem 4

Jada rewrites \(5 \boldcdot 3^x\) as \(15x\). Do you agree with Jada that these are equivalent expressions? Explain your reasoning.

### Solution

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### Problem 5

Investment account 1 starts with a balance of $200 and doubles every year. Investment account 2 starts with $1,000 and increases by $100 each year.

- How long does it take for each account to double?
- How long does it take for each account to double again?
- How does the growth in these two accounts compare? Explain your reasoning.

### Solution

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### Problem 6

A study of 100 recent high school graduates investigates a link between their childhood reading habits and achievement in high school.

Participants are asked if they read books every night with another person when they were ages 2 to 5, as well as their grade average for all of their high school classes. The results are represented in the table.

read books nightly | did not read books nightly | |
---|---|---|

A average | 16 | 10 |

B average | 21 | 14 |

C average | 12 | 16 |

D average | 3 | 8 |

- What does the 21 in the table represent?
- What does the 10 in the table represent?

### Solution

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(From Unit 3, Lesson 1.)### Problem 7

Lin says that a snack machine is like a function because it outputs an item for each code input. Explain why Lin is correct.

### Solution

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(From Unit 4, Lesson 1.)### Problem 8

At a gas station, a gallon of gasoline costs $3.50. The relationship between the dollar cost of gasoline and the gallons purchased can be described with a function.

- Identify the input variable and the output variable in this function.
- Describe the function with a sentence of the form "\(\underline{\hspace {0.5in}}\) is a function of \(\underline{\hspace {0.5in}}\)."
- Identify an input-output pair of the function and explain its meaning in this situation.

### Solution

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(From Unit 4, Lesson 1.)