Answer:
a) u(x) =21.47°C
b) u(x) =27.53°C
Explanation:
This requires Newton's Law of Cooling. The formula is:
u(x) = T + (T₀ - T)×e^(kt)
Plugging in our information:
u(x) = 30 + (7- 30)×e^(kt)
u(x) = 30 - 23×e^(kt)
at temperature 16°C at time 2 min.
16 = 30 - 23×e^(2 k)
e^(2k) = 14/23
2k = ln(14/23)
k = - 0.248
Temperature at t= 4 minute
u(x) = 30 - 23×e^(-0.248×4)
u(x) =21.47°C
temperature at t = 9 min
u(x) = 30 - 23×e^(-0.248×9)
u(x) =27.53°C
