Posted by **Debbie** on Sunday, March 14, 2010 at 4:31am.

A cold metal bar at -30 degrees Celsius is submerged in a pool maintained at a temperature of 40 degrees Celsius. Half a minute later, the temperature of the bar is 20 degrees Celsius. How long will it take the bar to attain a temperature of 30 degrees Celsius?

I know that dy/dt=k(y-b) and y(t)=b+Ce^kt

- calculus -
**drwls**, Sunday, March 14, 2010 at 8:43am
The solution will be of the form

T - 40 = (-70)*exp(-kt)

Note that this satisfies T = -30 when t = 0 and T-> 40 as t -> infinity

Solve for k by using the fact that

T = 20 at t = 30 s.

-20 = -70*exp(-30 t)

exp(-30k) = 0.2857

-30k = -1.253

k = 4.18*10-2

(1/k) = 23.9 seconds

Now solve for t when T = 30 C

- Math -
**Mora**, Tuesday, December 13, 2016 at 9:16pm
I hate this

Doesn't help for me in any thing

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