Question

Comp. 2 Comp. 1 Comp. 3 3 Here are some formulas that may help for the following problem: 1 = Sxy/Sxx Sxy = -1; -7)(y-7) Bo = ý – Bit Sxx = -(*; -7) 4. (10 points) An engineer measures the growth rate of a substance by counting the number of cells N present at various times t as shown in the table below. t N 1 10 2 32 3 41 4 77 5 120 6 224 Let i = a ti, Int = = = Int;, N = 1 Ni, and In N = {In N; For the data above, we have the following: i = 1t; = 3.5 Int=- Int; = 1.0965 N= N; = 84 In N = D, In N; = 4.0041 and Eft-1)2 = 17.5 Di (ti - 1)(N; -N) = 685 Li (Int; - Int)2 = 2.1955 (t: -7)(In N; - In N) = 10.0704 -(N; -N)2 = 30974 - (Int; - Int)(N-1) = 215.7980 (In N; - In N)2 = 5.9797 (Int; – Int)(In N; - In N) = 3.5611 Fit the model N = 77 Estimate of Estimate of

Answer 1

DELTA PO NO model N= Yo e both In Yo sides taking kt let In N A B then equation becomes y = A t Bt error The re squared is given by Now à - Beki ( & (Yi - à t 5 t)? differentiating wise -25 (Y; - Å + ß 2) = 0 [Yi differentiating et 2 e² -2 & ti (y; - À ßti) = 0 Etiyi Iti + Ret? solving equation 0 ao llow Wist B âti unknown and B we eget B = Ilti-E) (Y;-)) & (tj -E)

Date/ DELTA Pg No E (ti substituting value of Y and E Centi & (ti-A) ² we get by solving the equation À 7 - Ê t JA Also, substituting values У and B m Yo Inn exp [ en N the Putning Calculated valves 10 0704 0.5755 175 Yo _ext 4.0041 0.5753-5) 7-3144 12 The firted model is N = o 5755 t 7-3144 e