You are designing a manufacturing process, and measure the cooling of a part after a key step in the process:. t (min) 01238 13 18 23 28 33 38 43 48 53 TC) 86 82 79 77 69 6257 53 49 47 44 42 40 39 You decide to model this cooling process as an exponential decay, of the form: T(t) = T0e^-ct a) Write the equation for the error e of the exponential decay approximation. b) Write the two linear equations that can be solved for the coefficient val- ues that minimize the error e. (Hint: You will need to make variable substitutions to obtain linear forms of these equations.) c) Write the equations from part (b) as a matrix equation of the form Ar = b. d) Solve in MATLAB to find the coefficient values for a least-squared error fit. e) Plot the data points along with the approximation fitting curve using the calculated coefficient values from part (e) on two different plots with different scaling for the T axis: i) t and T ii) t and In(T)