Solving for a variable in equation

I want to solve for t in the equation: Tf=Ts+(T0-Ts)*exp(-k*t), but I can't figure out how to solve for t. I can only solve for Tf. Here is my script. What do I need to add/change to solve for t?

T0=120;

Ts=38;

k=0.45;

Tf=65;

Tf=Ts+(T0-Ts)*exp(-k*t)

Answer 1

[Star Strider]

Use a root-finding function (I chose fzero here), then take the known variable values, create an anonymous function from the expression for ‘Tf’ and solve:

T0=120;
Ts=38;
k=0.45;
Tf=65;
% Tf=Ts+(T0-Ts)*exp(-k*t);

[tval,fval] = fzero(@(t) Ts+(T0-Ts)*exp(-k*t)-Tf, 1)

producing:

tval =
     2.4686

[Maddie Sanders]

Thank you!

What does tval and fval represent, and where did you get the valye of 1 in the parenthesis.

[Star Strider]

My pleasure!

The ‘tval’ output is the value of ‘t’ where the expression equals ‘Tf’, and the ‘fval’ output is the value of the function at that point, indicating that it found a ‘t’ value that resulted in the anonymous function being very close to zero (within the tolerance fzero uses). Every nonlinear parameter estimation function requires an initial estimate for the parameter (or parameters) it is estimating, and I chose 1 here. The initial parameter estimates can be important in some problems, however not in this one, where widely differing iinitial estimates all produce the same result for ‘tval’.

[Star Strider]

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