Finding Tau, physical chemistry help

I have a lab where we got a florescence decay curve over time using a oscilloscope. Now I have to determine 1/tau using the decay. But I dont know how. Is it only the slope of the initial decay. I know that kobserved = 1 /tau.

Here is what the actual lab question is asking me to do...

For each solution determine 1/tau ie k observed. using only the portion of the data that corresponds to fluorescence decay. Fluorescence intensity, I, is proportional to [A] for the equation can be written as I = I(0) * e^-1/tau, this process is pseudo first order

I can't go any farther with this lab until I know tau...any help would be great.

You made a tiny mistake. The first-order equation is:

I(f) = I(0)*e^-(t/τ)

the numerator in the exponential function is time and not the number 1. Now, with that in mind you can rearrange the equation in the following way:

I(f) = I(0)*e^-(t/τ)
[I(f)/I(0)] = e^-(t/τ)
Ln[I(f)/I(0)] = -(t/τ)

With the last form you can easily determine τ by plotting Ln[I(f)/I(0)] over t, where I(f) is the intensity data you collected at time t (where t > 0), and I(0) is the intensity data you collected at time = 0 sec. The absolute value of the slope of this line will be the reciprocal of τ

Good luck