MATLAB & Advanced Math & Mechanical Engineering, Possibly Linear Algebra Question Help needed

No i, ii, iii for this question

Only iv, v, vi

Non-Polynomial Models (Transforming" the Data) The four data points at right are measurements of the amount of popcorn kernels (y) left un-popped as a function of the time (x) you run your air-popper. You want to calibrate an analytic model y = f(x) for future corn-popping analyses. You're considering the following six models for f(x): xlo - N 4 - Nw us iv. f(x) = a x[sin(x)] for unknown coefficients a, b and c. V. f(x)= aebx - 5 for unknown coefficients a and b. vi. f(x) = ae3x 5 for unknown coefficient a. For EACH model (i) through (vi), complete both tasks A and B below: 12 pts (A) Solve the problem using the matrix-form method: Show me how you're analytically transforming" the model (if necessary) Write the problem out in matrix form: r = Y-AC Define the vector c in terms of the unknown(s) in the model Write out the values of all the elements in the vector Y and matrix A using the provided data Use c =A\Yin MATLAB to solve for the coefficients in c (to at least 4 significant figures) Substitute the coefficients back into the model to write out the final equation for the best-fit model f(x) 6 pts (B) IF POSSIBLE, show me how you solve the problem using the P = polyfit(X, Y, n) command (thereby skipping all the steps of creating the matrix form above!) Show me how you're analytically transforming" the model (if necessary) Write out explicitly what you use for vectors X and Y, and your choice for the value of n Use the polyfit command in MATLAB, and show explicitly how you use the output P to give you the required unknown(s) a, b and/or c. Substitute the coefficients back into the model to write out the final equation for the best-fit model f(x) Note: If you don't think you can use polyfit for that particular model, then explain why. Non-Polynomial Models (Transforming" the Data) The four data points at right are measurements of the amount of popcorn kernels (y) left un-popped as a function of the time (x) you run your air-popper. You want to calibrate an analytic model y = f(x) for future corn-popping analyses. You're considering the following six models for f(x): xlo - N 4 - Nw us iv. f(x) = a x[sin(x)] for unknown coefficients a, b and c. V. f(x)= aebx - 5 for unknown coefficients a and b. vi. f(x) = ae3x 5 for unknown coefficient a. For EACH model (i) through (vi), complete both tasks A and B below: 12 pts (A) Solve the problem using the matrix-form method: Show me how you're analytically transforming" the model (if necessary) Write the problem out in matrix form: r = Y-AC Define the vector c in terms of the unknown(s) in the model Write out the values of all the elements in the vector Y and matrix A using the provided data Use c =A\Yin MATLAB to solve for the coefficients in c (to at least 4 significant figures) Substitute the coefficients back into the model to write out the final equation for the best-fit model f(x) 6 pts (B) IF POSSIBLE, show me how you solve the problem using the P = polyfit(X, Y, n) command (thereby skipping all the steps of creating the matrix form above!) Show me how you're analytically transforming" the model (if necessary) Write out explicitly what you use for vectors X and Y, and your choice for the value of n Use the polyfit command in MATLAB, and show explicitly how you use the output P to give you the required unknown(s) a, b and/or c. Substitute the coefficients back into the model to write out the final equation for the best-fit model f(x) Note: If you don't think you can use polyfit for that particular model, then explain why