Originally Posted by

**topsquark** The problem is we don't know the temperature of the water bath, so we can't finish the problem. I presume there was a typo in the problem and that you have this value. (If you don't, the problem can't be solved numerically.) But I'll set it up for you.

We first need to find k.

t = 5 min

To = 98 C, T = 38 C

38 - Ts = (98 - Ts)*e^(-k*5)

(38 - Ts)/(98 - Ts) = e^(-5k)

You can solve this for k. (Hint use log to the base e, or "ln" instead of log to the base 10.)

For the egg to reach 20 C we have

To = 38 C, T = 20 C (We need to find "how much longer," so I'm resetting the clock)

20 - Ts = (38 - Ts)*e^(-k*t) <-- Using the k value above.

Which you can solve now for t.

If you aren't given a value for Ts, then the solution is

t = 5*{ln[(38-Ts)/(20-Ts)]}/{ln[(98-Ts)/(38-Ts)]}

or you can write this as:

t = 5*[ln(38-Ts) - ln(20-Ts)]/[ln(98-Ts) - ln(38-Ts)]

-Dan