I am trying to solve at which x-values the function takes a given y
value. In its most simplistic case, this is easy to get with Solve:
sage: var('t')
sage: y=1-e**(-t/5)
sage: sol = solve(y==0.632,t)
sage: n(sol[0].rhs())
Which gives me 4.9983, the value I was looking for is 5, so it is OK.
However, in more complicated expressions (a biexponential of the from:
sage: y=-17.6666666666666*(e^(-1/5*t) - 1)*e^(-3.33333333333333*t
+0.971148468732930)
which varies between 0 an 1 in the interval between x=0 and x=5, the
task becomes complicated:
Trying to get the value at which the functions is 20% of its maximum I get
sage: solve(y==.2,t)
sage: [e^(1/5*t) == 265*e^(-10/3*t + 3467/3570)/(265*e^(-10/3*t +
3467/3570) - 3)]
which is indeed another equation which depends on t?
I am doing something wrong here? Is the command Solve adequate to solve
this kind of task?
Thank you very much in advance!
Jose
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