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practical

Fitting of second degree and exponential curves. practical. Fitting of second degree curve Prob.-. Fit the second degree curve for the above data. Solution- Let the second degree curve be y=a+bx+cx 2 ---------------------(1)

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practical

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  1. Fitting of second degree and exponential curves. practical

  2. Fitting of second degree curve • Prob.- Fit the second degree curve for the above data. Solution- Let the second degree curve be y=a+bx+cx2 ---------------------(1) By changing variable x to u=x-x , eq. (1) becomes y=a'+b'u+c'u2 ---------------------(2)

  3. Claim-To find a' ,b' & c'. The normal eq.s to find a' ,b' & c' are ∑y=na'+b'∑u+c'∑u2 -------------(3) ∑uy= a'∑u+b'∑u2+c'∑u3 -----------(4) ∑u2y= a'∑u2+b'∑u3+c'∑u4 ----------(5) Obtain the values of ∑y, ∑uy, ∑u2y ,∑u , ∑u2 , ∑u3 & ∑u4 . Use these values in eq. (3),(4) & (5) to get a' ,b' & c'. Put the values of u, a' ,b' & c‘ in eq. (2) , we get the required second degree curve.

  4. a‘=31.9143 ,b' =5.3, c' =0.6429 Here x = 3 Let u=x-x =x-3

  5. Prob.-Fit second degree curve.

  6. 2) Fitting of exponential curve y=a bX Prob.- Fit the exponential curve y=a bX for the above data. Solution-

  7. Let the exponential curve be y=a bX ---------------------(1) Taking log (to the base 10) of both sides. log (y)=log(a)+xlog(b) V=A+BX ,Where log (y)=v, log(a)=A, log(b)=B By changing variable x to u=(x-x)/10 we get v=A +Bu-----------------------(2) Then eq.(1) becomes y=a bu ---------------------(3) The normal eq.s to find A & B are ∑v=n A+ B ∑u -------------(4) ∑uv= A∑u+B∑u2-----------(5)

  8. Obtain the values of ∑v, ∑uv, ∑u , ∑u2 . Use these values in eq. (4),(5) to get A & B. Taking antilog of A & B we get a & b. putting u, a & b values in eq. (3) we get required eq.

  9. A=2.3105,B=0.08295 a=204.41,b=1.2105 Here x = 1971 Let u=(x-x )/10=(x-1971)/10

  10. Prob.-Fit the curve y=a bX

  11. 3) Fitting of exponential curve y=a ebx Prob.- Fit the exponential curve y=a ebx for the above data. Solution-

  12. Let the exponential curve be y=a ebx ---------------------(1) Taking log (to the base 10) of both sides. log (y)=log(a)+bxlog(e) u=A+BX --------------------------(2) Where log (y)=u, log(a)=A, blog(e)=b x 0.4343=B The normal eq.s to find A & B are ∑u=n A+ B ∑x -------------(3) ∑ux= A∑x+B∑x2-----------(4)

  13. Use eq. 3 & 4 ,find the values of A & B . Then a= antilog (A), b=B/0.4343 Put these values of a & b in eq. 1 we get required curve. A= -0.25347, B= 0.4617 a= 0.5578, b= 1.063

  14. Prob.-Fit the curve y=a ebx

  15. Prob.-Fit second degree & the curve y=a ebx ,y=a bX Prob.-Fit second degree & the curve y=a bX Prob.-Fit second degree curve & curve y=a ebx ,y=a bX

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