Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Solve for t such that Tmix(t) = 100 degree F
Tmix(t) = 72 + 65.8e^-0.125(t-tmilk)
tmilk = 1.826
k = 0.125
![The equation provided in the text relates to calculating the time \( t_2 \) for a process involving the mixing temperature \( T_{\text{mix}}(t) = 100^\circ F \). The text suggests proving algebraically that:
\[
t_2 = t_{\text{milk}} + \frac{1}{k} \ln \left[ \frac{4}{63} \left(49e^{-kt_{\text{milk}}} - 2\right) \right]
\]
Additionally, it is noted that:
- \( t_{\text{milk}} \) represents a specific time associated with milk.
- \( k \) is a constant that needs to be determined from previous calculations.
- The expression involves logarithmic and exponential components.
The instruction emphasizes using the previously calculated value of \( k \) and ensuring that all steps in the derivation are clearly shown.](https://content.bartleby.com/qna-images/question/4e3da8d7-5e45-4b35-92f7-ecdb5bd91ee7/cc2c6280-9f95-425d-bd9f-a67d4094de2e/4sy8c18_processed.jpeg)
Transcribed Image Text:The equation provided in the text relates to calculating the time \( t_2 \) for a process involving the mixing temperature \( T_{\text{mix}}(t) = 100^\circ F \). The text suggests proving algebraically that:
\[
t_2 = t_{\text{milk}} + \frac{1}{k} \ln \left[ \frac{4}{63} \left(49e^{-kt_{\text{milk}}} - 2\right) \right]
\]
Additionally, it is noted that:
- \( t_{\text{milk}} \) represents a specific time associated with milk.
- \( k \) is a constant that needs to be determined from previous calculations.
- The expression involves logarithmic and exponential components.
The instruction emphasizes using the previously calculated value of \( k \) and ensuring that all steps in the derivation are clearly shown.
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