Exponential warm

Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt).

If we placed jello salad at 30 degrees Fahrenheit in a room with 68 degrees F, 5 mins later became 44 degrees F, what would be its temperature after 10 mins?

Correct answer:

T3 =  52.8421 °F

Step-by-step explanation:

T0=30 °F T1=44 °F T2=68 °F  t1=5 min  T1 = T2  (T2T0)   e k   t1   e k   t1 = (T2T1)/(T2T0)  k   t1 = ln  T2T0T2T1  k=ln(T2T0T2T1)/t1=ln(68306844)/50.0919  t0=0 min T0=T2(T2T0) ek t0=68(6830) e(0.0919) 0=30 °F  t5=5 min T5=T2(T2T0) ek t5=68(6830) e(0.0919) 5=44 °F  t8=1000 min T8=T2(T2T0) ek t8=68(6830) e(0.0919) 1000=68 °F  t3=10 min T3=T2(T2T0) ek t3=68(6830) e(0.0919) 10=191004°F=52.8421°F



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