Question

Answer:

7. A cup of boiling water is placed outside at 1:00 PM. One minute later the temperature of the water is 152°F. After another minute its temperature is 112°F. What is the outside temperature?

Answer 1

Solis Hence The function of the temperature at any time t is given as T(+) - Ta+ (To-Tee-kt - o Where Ta is the outside temperature and. To is the initial temperature. To = 212° (boiling water constart). TH)= Tat (To-Tage kt Tlt) = Ta+(212-Tadeki Given, at tal, Tit) = T(I) = 152 152 = Tat(212-Tale" 152- Ta = (212-Tallek) Griven, at t=2 T(t) =T(2) = 112 112 = Tat (212-7a)e K(2) 112 - Ta = (212 -Talle 2K) —

ean Ⓡ Then = ean 112-Ta 152-Ta = (212-Ta) (e 2k) (212-Ta) (ek) 112-Tak - . 152-ta Substitute this value of ek into the past eqn, we get 152 - Ta = (212-T) (157724) (152 -Ta)(152-Ta) = (212-Ta) (112-Ta), (152-Ta)? = (212-7a) (112-Ta), 23104 + T&_30472 = 23744 - 3247a+va 324Ta - 304Ta = 23744~23104 20 Ta = 640 20 Ta = 32. .: The outside temperature is 32°F =o=