The Raven and the Jug
1. Referring only to your In-Out table, explain how things are changing (how does your “Out” change as your “In” changes?). Be sure to use your data in your response.
The output changes by increasing as the input also increases. I can tell this because the next consecutive in the system becomes larger than the previous one, in both the input number and the output number.
2. Is your In-Out Table an example of function? Explain why or why not.
The In-Out Table is not an example of a function because there is no specific rule that applies to the data. It increases by .2 cm, and then by .4 cm, and .4cm again, and then by .1cm. But if I were to try to make a function that corresponds with the table above, it would have to be something along the lines of every third number adds .2cm to the container (including the first one), and the numbers in between would increase the water depth by .4cm.
3. How could you use your results (In-Out table or Graph) to obtain an “Out” value for an “In” value you did not measure. Your “In” value could be between two data points you did measure (interpolation) or beyond your measured “In” values (extrapolation). Give an example using your method and your experiment results.
I could use the results of the graph to obtain and 'out' value for an 'in' value not measured by looking for the rough estimation of where the point would be in the graph, if it was one already in the measured part of the graph, and eyeing it to come to the closest estimate.
4. Explain how you chose to draw a straight line through your data points. If you ignored any data points, explain why.
I somewhat ignored the points that only increased by .2cm because if I were to include those points I would be missing out on even more variables.
5. Estimate the slope of the line you drew on your graph. What are the units of this slope?
The units of the slope, or the closest thing I received to the slope of the line, would be an increase of .104 cm every marble dropped inside the jar.
6. How could you change your experiment so that your data would result in a line with a steeper slope? If this is not possible, explain why.
This experiment cannot acquire a steeper slope because the data does not change even when done multiple times.
7. How could you change your experiment so that your data would result in a line with a flatter slope? If this is not possible, explain why.
Another reason why this experiment cannot change, that includes trying to get a flatter slope, is because each marble will increase the water depth by a certain degree, making it have an almost constant increase of marbles.
8. How could you change your experiment so that your data would result in a line with the same slope but above the line you drew (parallel and above)? If this is not possible, explain why.
This could happen by increasing the amount of water in the beginning, meaning instead of having a starting output of 6.3cm, it should start with 6.5cm instead.
9. How could you change your experiment so that your data would result in a line with the same slope but below the line you drew (parallel and below)? If this is not possible, explain why.
This is possible by decreasing the amount of water int the beginning, meaning instead of having a starting output of 6.3cm, it would start with 6cm instead.
10. Explain how you might obtain the rule that describes how your line takes “In” values (on the x-axis) and maps them to “Out” values (on the y-axis). Another way of phrasing this question is: How can you obtain the equation of your line? Challenge: Explain at least three ways.
There is no certain equation to find output with only the input given taking into consideration the unpredictable numbers the output has received. However, if I were to change some of the outputs by adding .1cm to and output, I may come up with a bearably equation. The equation would be the input, if easily divisible by 30, .2cm added to the previous number on the In-Out Table. If not easily divisible by 30, .4cm would be added to the previous number on the In-Out Table. The challenge option would be very difficult to achieve because we had to change an output just to come up with this equation, so to find three would be near impossible with someone of my intelligence.
The output changes by increasing as the input also increases. I can tell this because the next consecutive in the system becomes larger than the previous one, in both the input number and the output number.
2. Is your In-Out Table an example of function? Explain why or why not.
The In-Out Table is not an example of a function because there is no specific rule that applies to the data. It increases by .2 cm, and then by .4 cm, and .4cm again, and then by .1cm. But if I were to try to make a function that corresponds with the table above, it would have to be something along the lines of every third number adds .2cm to the container (including the first one), and the numbers in between would increase the water depth by .4cm.
3. How could you use your results (In-Out table or Graph) to obtain an “Out” value for an “In” value you did not measure. Your “In” value could be between two data points you did measure (interpolation) or beyond your measured “In” values (extrapolation). Give an example using your method and your experiment results.
I could use the results of the graph to obtain and 'out' value for an 'in' value not measured by looking for the rough estimation of where the point would be in the graph, if it was one already in the measured part of the graph, and eyeing it to come to the closest estimate.
4. Explain how you chose to draw a straight line through your data points. If you ignored any data points, explain why.
I somewhat ignored the points that only increased by .2cm because if I were to include those points I would be missing out on even more variables.
5. Estimate the slope of the line you drew on your graph. What are the units of this slope?
The units of the slope, or the closest thing I received to the slope of the line, would be an increase of .104 cm every marble dropped inside the jar.
6. How could you change your experiment so that your data would result in a line with a steeper slope? If this is not possible, explain why.
This experiment cannot acquire a steeper slope because the data does not change even when done multiple times.
7. How could you change your experiment so that your data would result in a line with a flatter slope? If this is not possible, explain why.
Another reason why this experiment cannot change, that includes trying to get a flatter slope, is because each marble will increase the water depth by a certain degree, making it have an almost constant increase of marbles.
8. How could you change your experiment so that your data would result in a line with the same slope but above the line you drew (parallel and above)? If this is not possible, explain why.
This could happen by increasing the amount of water in the beginning, meaning instead of having a starting output of 6.3cm, it should start with 6.5cm instead.
9. How could you change your experiment so that your data would result in a line with the same slope but below the line you drew (parallel and below)? If this is not possible, explain why.
This is possible by decreasing the amount of water int the beginning, meaning instead of having a starting output of 6.3cm, it would start with 6cm instead.
10. Explain how you might obtain the rule that describes how your line takes “In” values (on the x-axis) and maps them to “Out” values (on the y-axis). Another way of phrasing this question is: How can you obtain the equation of your line? Challenge: Explain at least three ways.
There is no certain equation to find output with only the input given taking into consideration the unpredictable numbers the output has received. However, if I were to change some of the outputs by adding .1cm to and output, I may come up with a bearably equation. The equation would be the input, if easily divisible by 30, .2cm added to the previous number on the In-Out Table. If not easily divisible by 30, .4cm would be added to the previous number on the In-Out Table. The challenge option would be very difficult to achieve because we had to change an output just to come up with this equation, so to find three would be near impossible with someone of my intelligence.