calculus
posted by Debbie .
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(yb) and y(t)=b+Ce^kt

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*102
(1/k) = 23.9 seconds
Now solve for t when T = 30 C 
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