Acake is removed from a 350◦f oven and placed on a cooling rack in a 70◦f room. after 30 minutes the cake is 200◦f. when will it be 100◦f?

350 F to 100 F it take approx 87.33 min  

Explanation:

given data

oven = 350◦F

cooling rack = 70◦F

time = 30 min

cake = 200◦F

solution

we apply here Newtons law of cooling  

= -k(T-Ta)

= (T(t) -Ta)

= = -k(T-Ta)

-ky = -ky

T(t) -Ta = (To -Ta) T(t) = Ta+ (To -Ta)  

put her value for time 30 min and T(t) = 200◦F and To =350◦F  and Ta = 70◦F

so here

200 = 70 + ( 350 - 70 )

k = 0.025575

so here for  T(t) = 100F

100 = 70 + ( 350 - 70 )

time = 87.33 min

so here 350 F to 100 F it take approx 87.33 min  

god i hope this !