16000=70000e to the power of (-a)(t) where t equals 3????

I had one of thse days, yesterday....

My advice???......back away from the computer......SLOWLY

$$\\16000=70000e^{-at}\qquad where\;\; t=3\\\\
16000=70000e^{-3a}\\\\$$

you cannot do any more unless you have a value for a

16000  =  70000e^(-3a)

Divide both sides by 70000:

8/35  =  e^(-3a)

Take the ln of both sides:

ln(8/35)  =  ln(e^(-3a))

Exponents come out as multipliers:

ln(8/35)  =  -3a ·ln(e)                                   ln(e)  =  1

ln(8/35)  =  -3a

a  =  ln(8/35) / -3     ≈     .4919688...

Doh! again.

This must be my Doh! day.

Good advice Chris.

My question I just asked Alan will most likely be my next Doh! moment.    

You know, sometimes when you are doing something really well it is easier just to roll with it.  

(Like when you roll the body in the carpet to hide the evidence of a terribly dumb m****r)  :)