Help with inverse problem, please?

• Mar 11th 2008, 07:50 PM
miyosuke
Help with inverse problem, please?
The function is C(a)=0.824(1.084)^a in terms of a. The inverse of C(a) can be used to determine a as a function of C. Now the thing is, I have a problem figuring out the function of a in terms of C.

C(a)=.824(1.084)^a
A(c)= C^-1

I just need help starting off this problem. Thanks!
• Mar 11th 2008, 08:17 PM
mr fantastic
Quote:

Originally Posted by miyosuke
The function is C(a)=0.824(1.084)^a in terms of a. The inverse of C(a) can be used to determine a as a function of C. Now the thing is, I have a problem figuring out the function of a in terms of C.

C(a)=.824(1.084)^a
A(c)= C^-1

I just need help starting off this problem. Thanks!

You need to solve $\displaystyle C = 0.824\, (1.084)^a$ for a. Take ln of both sides:

$\displaystyle \ln C = \ln \left[ \, 0.824\, (1.084)^a \, \right] = \ln 0.824 + \ln (1.084)^a = \ln 0.824 + a \ln 1.084$.

This has the form $\displaystyle \ln C = A + B a$:

$\displaystyle a = \frac{\ln (C) - A}{B} = ....$