148k views
1 vote
PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT

PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT-example-1
User Papacostas
by
7.9k points

1 Answer

5 votes

Since the room temperature is 22 degrees Celsius,


(dT)/(dt)=k(T-22)

Solving the differential equation,


(1)/(T-22) dT=k dt \\ \\ \int (1)/(T-22) dT=\int k dt \\ \\ \ln|T-22|=kt+C

When t=0, the temperature is 100 degrees.


\ln 78=C \\ \\ \implies \ln|T-22|=kt+\ln 78

When t=1, the temperature is 80 degrees.


\ln 58=k+\ln 78 \implies k=\ln(29/39) \\ \\ \implies \ln|T-22|=t \ln(29/39)+\ln 78

Setting t=4,


\ln|T-22|=4\ln(29/39)+\ln 78 \\ \\ T=22+e^(4\ln(29/39)+\ln 78) \approx \boxed{46}

User Gberth
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories