Jodi pouring herself a cold soda that has an initial initial temperature of 37 d

Question

Jodi pouring herself a cold soda that has an initial initial temperature of 37 degrees Fahrenheit and immediately

went outside to sunbathe where the temperature was a steady of 100 degrees Fahrenheit. after 7 Minutes the temperature of a soda was 43 degrees Fahrenheit. Jodi had to run back into the house to answer the phone. What was the expected temperature of the soda after an additional 11 minutes? please do not round until the final answer and then round to the nearest tenth as needed.

Score: 0 of 1 pt 5.5.18 Jodi poured herself a cold soda that had an initial termperature of 37 F and immediately went outside to sunbathe where the tem minutes the temperature of the soda was 43"F. Jodi had to run back into the house to answer the phone. What is the expected t addtional 11 minutes? (Denot round unti the final answer Then round to the nearest tenth as needed.) Enter your eniswer in the answer box and then cick Check Answer All parts showing

Explanation / Answer

applying newtons law of cooling formula

T(t) = Ta + ( To - Ta )e^kt

k = ln ( T(t) - Ta ) / (T0 - Ta ) / t

k = ln ( 43 - 100 ) / ( 37 - 100 ) / 7

k = -0.014297

temperature after additional 11 minutes

T(18) =  Ta + ( To - Ta )e^kt

= 100 + ( 37 - 100 ) e^(-0.014297* 18 )

= 51.3 degrees F

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