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write a function about ' v(t)=10^9+​10^8*(1-ex​p(-t./100)​)-1.5*10^7​*t '

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kris mere
kris mere 2011-11-15
[EDIT: 20111115 14:07 CST - merge duplicate - WDR]
question about matlab : I want to write a function about ' v(t)=10^9+10^8*(1-exp(-t./100))-1.5*10^7*t ' . In order to get each 't' , how can I write a function with 't' at the left side of the equal sign?(for example:t=......) Thanks for help!!
[Merge from duplicate]
I want to write a function about
v(t)=10^9+10^8*(1-exp(-t./100))-1.5*10^7*t
In order to get each 't' , how can I write a function with 't' at the left side of the equal sign?(for example : t = ......)
v(t)=10^9*(x./100)
x=(100:-5:40)
If I don't write a function with 't' at the left side of the equal sign, but I still have to write a to acquire each 't'.

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回答（3 个）

Walter Roberson
Walter Roberson 2011-11-15
If you have a particular v value and wish to solve for the corresponding t value, then the solution is
t = 100*LambertW(-(1/15)*exp((1/1500000000)*v-11/15))-(1/15000000)*v+220/3
LambertW is part of the Symbolic Toolbox, or you can use one of the contributions such as http://www.mathworks.com/matlabcentral/fx_files/6909/1/content/doc/lambertw.html
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Walter Roberson
Walter Roberson 2011-11-15
The solution for your rephrased question remains the same. At best the additional information tells you what value of v to use in the LambertW expression.
If you have the Symbolic Toolkit, the way to get this solution is:
syms v t
tsol = solve(10^9+10^8*(1-exp(-t./100))-3/2*10^7*t,t);
After that if you want to put in particular v, you can do that using subs(), such as
x=100:-5:40;
tnumeric = double( subs(tsol, v, 10^9*(x./100)) );
Myself, I find it difficult to understand how you can define v(t) in terms that do not involve t but do involve a previously unstated variable x.

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Daniel Shub
Daniel Shub 2011-11-15
I don't think you can. If you work through the math, I think you will eventually get something t+a*log(b*t) is equal to c. If you are willing to accept the approximation that t+a*log(b*t) is approximately t (for large enough t), then you can isolate t on the LHS.
Friedrich
Friedrich 2011-11-15
Hi,
risky (violates some basic rules of numerical mathematics) but should work in the most cases
func = @(t) 10^9+10^8*(1-exp(-t./100))-1.5*10^7*t;
x0 = 0;
v = 3000;
t = fzero(@(x) func(x) - v,x0)
func(t)

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