Newton's cooling law..

[venger]

1. The problem statement, all variables and given/known data
"A cup of hot chocolate, in a room temperature of 21*C, cools accordiing to Newton's law of cooling. Determine the rate of cooling, k, of the hot chocolate if it cools from 86*C to 65*C in 15 minutes"


2. Relevant equations
Newton's cooling law, ln function
T-Ts=(T. - Ts)e^(kt)


3. The attempt at a solution

T-Ts=(T. - Ts)e^(kt)
65-21=(86-21)e^(15k)
44=65e^(15k)
44/65=e^(15k)
ln(44/65)=15k
(ln(44/65))/15=k
k=-0.02601...
Is this right?

[ice109]

1. The problem statement, all variables and given/known data
"A cup of hot chocolate, in a room temperature of 21*C, cools accordiing to Newton's law of cooling. Determine the rate of cooling, k, of the hot chocolate if it cools from 86*C to 65*C in 15 minutes"


2. Relevant equations
Newton's cooling law, ln function
T-Ts=(T. - Ts)e^(kt)


3. The attempt at a solution

T-Ts=(T. - Ts)e^(kt)
65-21=(86-21)e^(15k)
44=65e^(15k)
44/65=e^(15k)
ln(44/65)=15k
(ln(44/65))/15=k
k=-0.02601...
Is this right?
were you taught this formula or the differential equation?

it's right btw