Answer:
y(t) = 17+70e^(-t/50)
Step-by-step explanation: The model of equation given is:
dy/dt = -1/50 (y-17)
Integrate both sides
dy/(y-17) = -1/50 dt
This lead to
ln(y-17) = -1/50 t + C
Log both sides:
y = c e^(-t/50) + 17 ....... (1)
and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 87°C.
87 = c e^0 + 17
e^0 = 1
Therefore c = 87-17 = 70
y(0) = 87, so c=70
Substitute c into equation 1. This lead to:
y(t) = 17+70e^(-t/50)
