Question

1. for a science project eli decided to study colonies of mold. he observed a piece of bread that was molding. the ratios represent the number of days passed to colonies of mold on the bread. create a table then graph and explain if the quantities are proportional to each other or not.

1 to 1
2 to 4
3:9
4/16
twenty five colonies were found on the fifth day.
graph
proportional or not? explain.

Explanation:

Table Creation

First, we interpret each ratio as (Number of Days, Number of Colonies):

• "1 to 1" means 1 day, 1 colony.
• "2 to 4" means 2 days, 4 colonies.
• "3 - 9" means 3 days, 9 colonies.
• "4/16" means 4 days, 16 colonies.
• "Twenty five colonies were found on the fifth day" means 5 days, 25 colonies.

Now we create the table:

Number of Days	Number of Colonies
2	4
3	9
4	16
5	25

Graphing (Brief Description)

To graph this, we can use a coordinate plane where the x - axis represents the number of days and the y - axis represents the number of colonies. We plot the points (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).

Proportional or Not? Explanation

For two quantities (days, let's call it \(x\), and colonies, let's call it \(y\)) to be proportional, the ratio \(\frac{y}{x}\) should be constant for all values of \(x\) and \(y\).

• For \(x = 1,y = 1\): \(\frac{y}{x}=\frac{1}{1}=1\)
• For \(x = 2,y = 4\): \(\frac{y}{x}=\frac{4}{2}=2\)
• For \(x = 3,y = 9\): \(\frac{y}{x}=\frac{9}{3}=3\)
• For \(x = 4,y = 16\): \(\frac{y}{x}=\frac{16}{4}=4\)
• For \(x = 5,y = 25\): \(\frac{y}{x}=\frac{25}{5}=5\)

Since the ratio \(\frac{y}{x}\) is not constant (it changes from 1 to 2 to 3 to 4 to 5), the number of days and the number of mold colonies are not proportional. However, we can observe that the number of colonies \(y=x^{2}\) (since \(1 = 1^{2}\), \(4=2^{2}\), \(9 = 3^{2}\), \(16=4^{2}\), \(25 = 5^{2}\)), so it is a quadratic relationship, not a proportional (linear) relationship.

Final Answer (Proportional or Not)

The quantities (number of days and number of mold colonies) are not proportional. This is because the ratio of the number of colonies to the number of days (\(\frac{\text{colonies}}{\text{days}}\)) is not constant (it is 1, 2, 3, 4, 5 for days 1 - 5 respectively), and the relationship between days and colonies follows \(y=x^{2}\) (a quadratic relationship) rather than a proportional (linear) relationship \(y = kx\) (where \(k\) is a constant).

Answer:

Table Creation

First, we interpret each ratio as (Number of Days, Number of Colonies):

• "1 to 1" means 1 day, 1 colony.
• "2 to 4" means 2 days, 4 colonies.
• "3 - 9" means 3 days, 9 colonies.
• "4/16" means 4 days, 16 colonies.
• "Twenty five colonies were found on the fifth day" means 5 days, 25 colonies.

Now we create the table:

Number of Days	Number of Colonies
2	4
3	9
4	16
5	25

Graphing (Brief Description)

To graph this, we can use a coordinate plane where the x - axis represents the number of days and the y - axis represents the number of colonies. We plot the points (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).

Proportional or Not? Explanation

For two quantities (days, let's call it \(x\), and colonies, let's call it \(y\)) to be proportional, the ratio \(\frac{y}{x}\) should be constant for all values of \(x\) and \(y\).

• For \(x = 1,y = 1\): \(\frac{y}{x}=\frac{1}{1}=1\)
• For \(x = 2,y = 4\): \(\frac{y}{x}=\frac{4}{2}=2\)
• For \(x = 3,y = 9\): \(\frac{y}{x}=\frac{9}{3}=3\)
• For \(x = 4,y = 16\): \(\frac{y}{x}=\frac{16}{4}=4\)
• For \(x = 5,y = 25\): \(\frac{y}{x}=\frac{25}{5}=5\)

Since the ratio \(\frac{y}{x}\) is not constant (it changes from 1 to 2 to 3 to 4 to 5), the number of days and the number of mold colonies are not proportional. However, we can observe that the number of colonies \(y=x^{2}\) (since \(1 = 1^{2}\), \(4=2^{2}\), \(9 = 3^{2}\), \(16=4^{2}\), \(25 = 5^{2}\)), so it is a quadratic relationship, not a proportional (linear) relationship.

Final Answer (Proportional or Not)

The quantities (number of days and number of mold colonies) are not proportional. This is because the ratio of the number of colonies to the number of days (\(\frac{\text{colonies}}{\text{days}}\)) is not constant (it is 1, 2, 3, 4, 5 for days 1 - 5 respectively), and the relationship between days and colonies follows \(y=x^{2}\) (a quadratic relationship) rather than a proportional (linear) relationship \(y = kx\) (where \(k\) is a constant).