Question

The differential equation that describes the temp T of a jug of orange juice t minutes after being taken out of a refrigerator into a 70 degree F room is $\frac{dT}{dt}= k(T-70)$

The temp of the juice starts out at 40 degrees F, one minute later the juices temp is up to 50 degrees F

Solve this initial value differential equation for T, k and a value for the integration constant.

Answer 1

Q. Given differential equation ат at k (1-70) T Temp of Jug of orange juice 70 of ambeint /sunrounding Temp. > at tro T = 40 of tal min T=50 F here AT at K (T-70) dT Sk k dt T-70 en (T-70) - Қt + c Kt с (T-70) e for e put too Та Чо O C e e e (10-70) -Borec T-70= -30 ek kt ке T= 70-30e to get K' put tal T=50 K 50 =70-30e zoek 20 70-50 ek مر مر ка en (213) = -0.40546 -0.Yosu6t 70-30e T