Jodi poured herself a cold soda that had an initial temperature 36 degrees F and immediately went outside to sunbathe where the temperature was a steady 99 degree F. After 5minutes the temperature of the soda was 46 degree F. Jodi had to run back into the house to answer the phone. What is the expected temperature of the soda after an additional 13 minutes?

Question

Mathematics

Maia

28 August, 20:14

Jodi poured herself a cold soda that had an initial temperature 36 degrees F and immediately went outside to sunbathe where the temperature was a steady 99 degree F. After 5minutes the temperature of the soda was 46 degree F. Jodi had to run back into the house to answer the phone. What is the expected temperature of the soda after an additional 13 minutes?

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Answers (1)

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Elle Liu · Answer 1

this can be solve using newtons heating of cooling

(Ts - T) = (Ts - To) * e^ (-kt)

Where Ts is the ambient temperature

To is initial temperature

T is the temperature at time t

t is the time

k is constant

fisrt solve the constant k for the given first scenario

(99 - 36) = (99 - 46) * e (-5k)

K = - 0.0346

Using k, solve T at t = 13 min

(99 - 46) = (99 - T) * e (-13 * (-0.0346)

T = 58.82 degree F