Suppose it is known that the coffee cools at a rate of 1degree C when its temperature is 70 degrees C. The room is 20degrees C. a) What does the differential equation become in thiscase? b) sketch a direction field and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? c) Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes
Freddy Friedman
Answered question
2022-07-27
Suppose it is known that the coffee cools at a rate of 1degree C when its temperature is 70 degrees C. The room is 20degrees C. a) What does the differential equation become in thiscase? b) sketch a direction field and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? c) Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes
Answer & Explanation
abortargy
Beginner2022-07-28Added 19 answers
first things first you need to solve for K from the original equation: dC/dt=-K( C-A) where A=ambient temp, C=coffee temp, Kneeds to be solved, dC/dt= rate of decline C=70, dC/dt= -1, A= 20 -1 = -K (70-20) K = -1/50 0=70 2mins = 70 + 2(-1/50(70-20)) = 68 4mins = 68 + 2(-1/50(68-20)) = 66.08 6mins = 66.082 + 2(-1/50(66.08-20)) = 64.24 8mins = 64.24 + 2(-1/50(64.24-20)) = 62.47 10mins = 62.47 + 2(-1/50(62.47-20)) = 60.77 you can also solve it for the actual value by inverting thedC/dt=-k(C-A) to get dt/dC = -50/(C-20)