# Lesson 2

Patterns of Growth

### Problem 1

A population of ants is 10,000 at the start of April. Since then, it triples each month.

1. Complete the table.
2. What do you notice about the population differences from month to month?
3. If there are $$n$$ ants one month, how many ants will there be a month later?
months since April number of ants
0
1
2
3
4

### Solution

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### Problem 2

A swimming pool contains 500 gallons of water. A hose is turned on, and it fills the pool at a rate of 24 gallons per minute. Which expression represents the amount of water in the pool, in gallons, after 8 minutes?

A:

$$500 \boldcdot 24 \boldcdot 8$$

B:

$$500 + 24 + 8$$

C:

$$500 + 24 \boldcdot 8$$

D:

$$500 \boldcdot 24^8$$

### Solution

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### Problem 3

The population of a city is 100,000. It doubles each decade for 5 decades. Select all expressions that represent the population of the city after 5 decades.

A:

32,000

B:

320,000

C:

$$100,\!000 \boldcdot 2 \boldcdot 2 \boldcdot 2 \boldcdot 2 \boldcdot 2$$

D:

$$100,\!000 \boldcdot 5^2$$

E:

$$100,\!000 \boldcdot 2^5$$

### Solution

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### Problem 4

The table shows the height, in centimeters, of the water in a swimming pool at different times since the pool started to be filled.

1. Does the height of the water increase by the same amount each minute? Explain how you know.
2. Does the height of the water increase by the same factor each minute? Explain how you know.
minutes height
0 150
1 150.5
2 151
3 151.5

### Solution

For access, consult one of our IM Certified Partners.

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 4.)