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山无语

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[求助] 求大神们帮我解一下方程吧，高中数学都还给老师了已有2人参与

3.53=A/（1+B*EXP(-K*52)
6.17=A/（1+B*EXP(-K*67)
16.34=A/（1+B*EXP(-K*82)

就是三个未知数三个方程，可是我忘了怎么求exp了，求大神给个公式吧，就是A=公式，B=公式，K=公式，方便我算其他组的数据，万分感谢啊。

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1楼 2015-11-12 10:57:34

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

wurongjun

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【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
感谢参与，应助指数 +1
山无语: 金币+20 2015-11-12 13:10:42

建议用Matlab解！
>> syms K B A
>> f1=3.53-A/(1+B*exp(-K*52))

f1 =

353/100-A/(1+B*exp(-52*K))

>> f2=6.17-A/(1+B*exp(-K*67))

f2 =

617/100-A/(1+B*exp(-67*K))

>> f3=16.34-A/(1+B*exp(-K*82))

f3 =

817/50-A/(1+B*exp(-82*K))

>> [A B K]=solve(f1,f2,f3,'A','B','K')

A =

[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]
[ -595405/261484]

B =

[                                                    -37620240668060376629248/1577379504542829242672938041*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(cos(2/15*pi)+i*cos(11/30*pi))^7*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(cos(4/15*pi)+i*cos(7/30*pi))^7*119667^(8/15)*143792^(7/15)]
[  -37620240668060376629248/1577379504542829242672938041/(1/4*5^(1/2)-1/4+1/4*i*2^(1/2)*(5+5^(1/2))^(1/2))^7*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(-cos(7/15*pi)+i*cos(1/30*pi))^7*119667^(8/15)*143792^(7/15)]
[                            -37620240668060376629248/1577379504542829242672938041/(-1/2+1/2*i*3^(1/2))^7*119667^(8/15)*143792^(7/15)]
[ -37620240668060376629248/1577379504542829242672938041/(-1/4*5^(1/2)-1/4+1/4*i*2^(1/2)*(5-5^(1/2))^(1/2))^7*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(-cos(1/15*pi)+i*cos(13/30*pi))^7*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(-cos(1/15*pi)-i*cos(13/30*pi))^7*119667^(8/15)*143792^(7/15)]
[ -37620240668060376629248/1577379504542829242672938041/(-1/4*5^(1/2)-1/4-1/4*i*2^(1/2)*(5-5^(1/2))^(1/2))^7*119667^(8/15)*143792^(7/15)]
[                            -37620240668060376629248/1577379504542829242672938041/(-1/2-1/2*i*3^(1/2))^7*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(-cos(7/15*pi)-i*cos(1/30*pi))^7*119667^(8/15)*143792^(7/15)]
[  -37620240668060376629248/1577379504542829242672938041/(1/4*5^(1/2)-1/4-1/4*i*2^(1/2)*(5+5^(1/2))^(1/2))^7*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(cos(4/15*pi)-i*cos(7/30*pi))^7*119667^(8/15)*143792^(7/15)]
[                   -37620240668060376629248/1577379504542829242672938041/(cos(2/15*pi)-i*cos(11/30*pi))^7*119667^(8/15)*143792^(7/15)]

K =

[                                                 -log(1/143792*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(cos(2/15*pi)+i*cos(11/30*pi))*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(cos(4/15*pi)+i*cos(7/30*pi))*119667^(1/15)*143792^(14/15))]
[  -log(1/143792*(1/4*5^(1/2)-1/4+1/4*i*2^(1/2)*(5+5^(1/2))^(1/2))*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(-cos(7/15*pi)+i*cos(1/30*pi))*119667^(1/15)*143792^(14/15))]
[                            -log(1/143792*(-1/2+1/2*i*3^(1/2))*119667^(1/15)*143792^(14/15))]
[ -log(1/143792*(-1/4*5^(1/2)-1/4+1/4*i*2^(1/2)*(5-5^(1/2))^(1/2))*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(-cos(1/15*pi)+i*cos(13/30*pi))*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(-cos(1/15*pi)-i*cos(13/30*pi))*119667^(1/15)*143792^(14/15))]
[ -log(1/143792*(-1/4*5^(1/2)-1/4-1/4*i*2^(1/2)*(5-5^(1/2))^(1/2))*119667^(1/15)*143792^(14/15))]
[                            -log(1/143792*(-1/2-1/2*i*3^(1/2))*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(-cos(7/15*pi)-i*cos(1/30*pi))*119667^(1/15)*143792^(14/15))]
[  -log(1/143792*(1/4*5^(1/2)-1/4-1/4*i*2^(1/2)*(5+5^(1/2))^(1/2))*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(cos(4/15*pi)-i*cos(7/30*pi))*119667^(1/15)*143792^(14/15))]
[                   -log(1/143792*(cos(2/15*pi)-i*cos(11/30*pi))*119667^(1/15)*143792^(14/15))]

>> double(A)

ans =

-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770
-2.2770

>> double(B)

ans =

  -3.1094
3.0415 + 0.6465i
  -2.8406 - 1.2647i
2.5156 + 1.8277i
  -2.0806 - 2.3108i
1.5547 + 2.6928i
  -0.9609 - 2.9572i
0.3250 + 3.0924i
0.3250 - 3.0924i
  -0.9609 + 2.9572i
1.5547 - 2.6928i
  -2.0806 + 2.3108i
2.5156 - 1.8277i
  -2.8406 + 1.2647i
3.0415 - 0.6465i

>> double(C)
??? Undefined function or variable 'C'.

>> double(K)

ans =

0.0122
0.0122 - 0.4189i
0.0122 - 0.8378i
0.0122 - 1.2566i
0.0122 - 1.6755i
0.0122 - 2.0944i
0.0122 - 2.5133i
0.0122 - 2.9322i
0.0122 + 2.9322i
0.0122 + 2.5133i
0.0122 + 2.0944i
0.0122 + 1.6755i
0.0122 + 1.2566i
0.0122 + 0.8378i
0.0122 + 0.4189i

>> A(1)

ans =

-595405/261484

>> double([A(1);B(1);K(1)])

ans =

-2.2770
-3.1094
0.0122
最后的是实数解！

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善恶到头终有报,人间正道是沧桑.

4楼2015-11-12 11:28:45