0
$\begingroup$

I have 3 nonlinear equations in 3 unknowns,

$\Large A=\frac{P_L}{1-c}\quad B=\frac{P_L}{1-ce^{-10k}}\quad C=\frac{P_L}{1-ce^{-20k}}$

where $A$, $B$, $C$ are known values and $P_L$, $c$ and $k$ are unknowns. I want to get them into one single equation in one of three unknowns ($P_L$, $c$ or $k$, does not matter) so I can use one of the root finding methods to determine that single unknown.

$\endgroup$
1
  • 1
    $\begingroup$ Put $x = e^{-10k}$ then between the first two equations you can show $c=\frac{(B-A)}{(Bx-A)}$. Use the second and third equations to write $\frac{B}{C}$ in terms of c and x. Now sub in your expression for c and multiply out to get a quadratic in x. $\endgroup$
    – Paul
    Dec 19 '20 at 21:32
2
$\begingroup$

You have $$c=1-\frac{P}{A}$$

$$ce^{-10k}=1-\frac{P}{B}$$ $$ce^{-20k}=1-\frac{P}{C}$$

Therefore $$(1-\frac{P}{B})^2=(1-\frac{P}{A})(1-\frac{P}{C})$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.