A pie cools in a 70 degree room. The pie is 300 degrees. After ten minuites the pie cools to 260 degrees

Question

Create a formula then find the temp of the pie after 120 minuites 

Answer 1

here's something to help you:

NEWTON’S LAW OF COOLING
Example (p. 436, Thomas/Finney 8th edition)
A hard-boiled egg at 98^o C is put into a sink of 18^o C water. After 5 minutes, the egg’s temperature is 38^o C. Assuming that the water in the sink increased negligibly in temperature, how much longer does it take for the egg’s temperature to become 20^o C?
Formula:T - T_s = (T₀ - T_s)e^-kt

where T = temperature of object at time t, T_s = temperature of surrounding medium (constant), & T₀ is initial temperature of object at time t=0.

Solution: We find how long it takes the egg to cool from 98 to 20, and then subtract the five minutes that already elapsed.
T – 18 = (98 – 18)e^-kt
T = 18 + 80e^-kt ← Equation A.

To find k, we use T = 38 when t = 5:
which leads to

The egg’s temp 20^o is substituted into Equation A:
20 = 18 + 80e^-0.28t which leads to t = 13 min.

After subtracting the earlier elapsed 5 minutes, we have the answer: 8 min.