# Solving for constants

• Oct 17th 2012, 07:03 AM
algorithm
Solving for constants
Hi,

I have the following equation:

$\displaystyle x(t) = ABexp(BCt)$

I also have a graph of $\displaystyle x(t)$ plotted against $\displaystyle t$. I should determine the constants $\displaystyle A, B, C$ using the equation and the graph.

How should I approach this problem? I was thinking of obtaining three equations using three data points from the graph.

Thanks.
• Oct 17th 2012, 07:50 AM
ebaines
Re: Solving for constants
If A, B, and C are constants then AB is a constant (let's call it 'D') and also BC is a constant (call it 'F'). So the equation is better written as $\displaystyle x(t) = De^{Ft}$. You can find the value for D using the value of x(t) at t=0, since x(0) = D. Then if there is at least one other point on the graph where for a known value of 't' you know the value for x(t), you can determine the value for F using the relationship $\displaystyle F = \frac {\ln(x(t))-ln(D)}{t}$.
• Oct 17th 2012, 10:21 AM
algorithm
Re: Solving for constants
Hi,

Thanks. I've come to a hurdle as my equation is a bit more complex:

$\displaystyle x(t) = [(A + B)/AB] * exp[At/C]$

What I have done so far is:

Let $\displaystyle K_{1} = [(A + B)/AB], K_{2}=A/C$, then using a graph of the function I get $\displaystyle K_{1} = 0.2, K_{2} = 1e-5$. I can't see where to go from here - where do I get a third equation from?

Thanks :)
• Oct 17th 2012, 10:56 AM
ebaines
Re: Solving for constants
You still have too many constants. You could set 'A' to whatever value you want, and then determine values for B and C from:

$\displaystyle B= \frac A {K_1 A-1}$

$\displaystyle C = \frac A {K_2}$

For example if you set A=1, then using your values for K1 amd K2 you get B = -1.25 and C = 1/(e-5).
• Oct 17th 2012, 11:04 AM
algorithm
Re: Solving for constants
Thanks.

The question asks me for the specific value of each of the three constants, so I can't set any constant to an arbitrary value.

I must have gone wrong somewhere in the working...will take a look.
• Oct 17th 2012, 02:45 PM
johnsomeone
Re: Solving for constants
What you need to look for is another relationship (i.e. equation) involving at least 2 of A, B, and C. The graph can *only* produce K1 and K2 for you, and you've already used it to determine them, so the graph will be of no further use to you.

Since you need it in exactly that form, with A, B, and C, those variables are meant to represent something. The additional relationship you seek (assuming the problem is properly defined), if not some explicit condition you've yet to mention, will likely come somehow from the meaning of the A, B, and C. The graph has done all it can for you.