# Rewriting a base; Formula of a Reciprocal Function

1. Sep 8, 2011

### ryao3688

1. The problem statement, all variables and given/known data

I have a function, y = 6*e^0.4x. How would I convert the regular form, y=a*e^bt to the form y= at^b?

2. Relevant equations

y = 6*e^0.4x

3. The attempt at a solution

I've tried to take the log of both sides, but if I do that, then "y" becomes a log, and I can't remove that "log*y" unless I put the "base" of the formula back down.

And another quick problem:

1. The problem statement, all variables and given/known data

I have a set of data, t and C (hours and concentration; g/L, respectively). Somehow, by using that data, I can solve for the concentration equation, 1/(a+bt).

2. Relevant equations

Given data:
t (h) 1.0 2.0 3.0 4.0 5.0
C (g/L) 1.43 1.02 0.73 0.53 0.38

Concentration equation, 1/(a+bt).

3. The attempt at a solution

Not a clue;I'm supposed to find the coefficients of the concentration equation by graphing the data that was received. I've tried to graph a graph of C vs. T, and tried to take the reciprocal of that equation, but it didn't work. I'm supposed to plot the above data in such a way, that the coefficients of the concentration formula can be solved. Any ideas on how I should go about finding the a/b values for the formula?

2. Sep 8, 2011

### wukunlin

let's say
$$A = e^a$$
then
$$e^{ab} = (e^a)^b = A^b$$

does that help?

3. Sep 8, 2011

### ryao3688

Thanks Wukunlin, but I know I can combine e with its exponent.
Let me just replace that "x" with "t".
Ie: y = 6e^0.4t can be written as y = 6(1.4918...)^t - I need to find a way to get the "t" next to the base, and somehow get the base as the exponent - in the form y = at^b. I'm just confused about how I should go about doing this.

4. Sep 8, 2011

### wukunlin

as far as I know that is impossible. What that does is turning an exponential function into a power function.