Jodi poured herself a cold soda that had an initial temperature of 44 degrees Fa

Question

Jodi poured herself a cold soda that had an initial temperature of 44 degrees Fahrenheit and immediately went outside to sunbath where the temperature was a steady 95 degrees Fahrenheit. after 8 minutes the temperature of the soda was 56° Fahrenheit. Jodi had to run back into the house to answer the phone so what is the expected temperature of the soda after an additional 13 minutes?

Homework: Module 12: Section 5.5 Homework Score: 0 of 1pt 5.5.18 8or 8 (8 complete) HW Score: 6563%, 525 of 8 pt Jod poured hersell a cold soda that had an inaial temperature of 4F and inmeãatoly went outside to sumbathe where the temperahire was a steaty 96'F Aber B minutes the tomperature of the soda was 56"F Jodi had to run back into the house to arawer the phone. What is the expected temperatiure of the soda atr Do not round untl the Sinal answer Then round to the nearest bunth as needed) Eter your answes in the answes box and then cick Check Answer All parts showng Or

Explanation / Answer

Solution:

As we know that

T(t) = Ta+(T0 - Ta)e^(-kt)
T0: original temperature, when t=0
T(t): the temperature of the given body at time t.
Ta: the temperature of surrounding air (ambient temperature)
k: proportionality constant
t: elapsed time

T0 = 44 F
Ta = 95 F

Now solve for k

solve for k
(T0 - Ta)e^(kt) = T(t) -Ta
e^(kt) = (T(t) -Ta)/(T0 - Ta)
kt = ln((T(t) -Ta)/(T0 - Ta))
k = ln((T(t) -Ta)/(T0 - Ta))/t

Plug T0 = 44 F
Ta = 95 F

t = 8 , T(8) = 56 F

k = ln((56 -95)/(44 - 95))/8  
k = -0.0335

Now for addtional 13 minutes

that t = 13 + 8 = 21

solve for T(21)
at = 18 min
T(18) = 95 + (44 - 95)e^(18*-0.0335)
T(18) = 67.1 F

Answer: 67.1 F

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