Question

1.) Suppose a network test showed the following relationship between app run time and the number of nodes in the network. Number of nodes (n) Run time – seconds (t) 200 29 500 58 1000 175 1500 729 2000 1458 2500 2479 3000 4375 4000 12250 a.) Plot the points on Desmos.com/calculator (copy/paste the table into equation field or choose Add Item – table on Desmos and type in the points in the table above). Desmos will assign variable names x1 and y1 to your data. Insert here the screenshot of your graph and a link to it (click on share your graph and copy the address from Share this link). b.) Consider the pattern – what type of function do you think would best model the data? Explain why. c.) Model your data using a quadratic function: I. Enter y1~ax1^2 + bx1 + c into a new equation field II. Write the given values for a, b and c: III. Using these values, write the function model in the form of t(n) = an^2 + bn + c. IV. Insert here a screenshot of your graph and a link to it. d.) Model your data using an exponential function I. Enter y1~ab^x1 into a new equation field II. Write the given values for a and b: III. Using these values, write the function model in the form of t(n) = ab^n: IV. Insert here a screenshot of your graph and a link to it. e.) Which regression model appears to provide a better fit? Hide the other one (click on the full circle beside the equation for the model). Insert here the screenshot of your graph and a link to it. f.) Estimate the run time if the number of nodes is 3500. Do the same for 6000 nodes. g.) Calculate dt/dn and evaluate it at n = 3500 and n = 6000. h.) Interpret the results – explain what they represent in the original context of the model.

          1.) Suppose a network test showed the following relationship between app run time and the number of nodes in the network.

Number of nodes (n)	Run time – seconds (t)
200	29
500	58
1000	175
1500	729
2000	1458
2500	2479
3000	4375
4000	12250

a.) Plot the points on Desmos.com/calculator (copy/paste the table into equation field or choose Add Item – table on Desmos and type in the points in the table above).
Desmos will assign variable names x1 and y1 to your data.
Insert here the screenshot of your graph and a link to it (click on share your graph and copy the address from Share this link).
b.) Consider the pattern – what type of function do you think would best model the data? Explain why.
c.) Model your data using a quadratic function:
I. Enter y1~ax1^2 + bx1 + c into a new equation field
II. Write the given values for a, b and c:
III. Using these values, write the function model in the form of t(n) = an^2 + bn + c.
IV. Insert here a screenshot of your graph and a link to it.
d.) Model your data using an exponential function
I. Enter y1~ab^x1 into a new equation field
II. Write the given values for a and b:
III. Using these values, write the function model in the form of t(n) = ab^n:
IV. Insert here a screenshot of your graph and a link to it.
e.) Which regression model appears to provide a better fit?
Hide the other one (click on the full circle beside the equation for the model).
Insert here the screenshot of your graph and a link to it.
f.) Estimate the run time if the number of nodes is 3500. Do the same for 6000 nodes.
g.) Calculate dt/dn and evaluate it at n = 3500 and n = 6000.
h.) Interpret the results – explain what they represent in the original context of the model.

1.) Suppose a network test showed the following relationship between app run time and the number of nodes in the network.

Number of nodes (n) Run time – seconds (t)
200 29
500 58
1000 175
1500 729
2000 1458
2500 2479
3000 4375
4000 12250

a.) Plot the points on Desmos.com/calculator (copy/paste the table into equation field or choose Add Item – table on Desmos and type in the points in the table above).
Desmos will assign variable names x1 and y1 to your data.
Insert here the screenshot of your graph and a link to it (click on share your graph and copy the address from Share this link).
b.) Consider the pattern – what type of function do you think would best model the data? Explain why.
c.) Model your data using a quadratic function:
I. Enter y1 ax1^2 + bx1 + c into a new equation field
II. Write the given values for a, b and c:
III. Using these values, write the function model in the form of t(n) = an^2 + bn + c.
IV. Insert here a screenshot of your graph and a link to it.
d.) Model your data using an exponential function
I. Enter y1 ab^x1 into a new equation field
II. Write the given values for a and b:
III. Using these values, write the function model in the form of t(n) = ab^n:
IV. Insert here a screenshot of your graph and a link to it.
e.) Which regression model appears to provide a better fit?
Hide the other one (click on the full circle beside the equation for the model).
Insert here the screenshot of your graph and a link to it.
f.) Estimate the run time if the number of nodes is 3500. Do the same for 6000 nodes.
g.) Calculate dt/dn and evaluate it at n = 3500 and n = 6000.
h.) Interpret the results – explain what they represent in the original context of the model.

Added by April W.

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