Question

A pot of stew is placed on a stove to heat. The temperature of the liquid reaches 170°F, and then the pot is taken off the burner and placed on a kitchen counter. The temperature of the air in the kitchen is 76°F.

If k = 0.34, the temperature of the liquid after 7 hours will be

ºF. (Hint: Use Newton’s cooling model.)

Answer 1

84.7 IS CORRECT

Explanation:

Answer 2

`T =84.7\°F`

Explanation:

Newton's cooling model is:

`T(t) =T_0 + (T_i-T_0)e^(-kt)`

Where

t is the time in hours

`T_0` is the ambient temperature

`T_i` is the initial temperature of the body

`k=0.34`

We know that:

`T_0=76\°F`

`T_i=170\°F`

Then after 7 hours the temperature of the liquid will be:

`T(7) =76 + (170-76)e^(-0.34(7))`

`T =84.7\°F`