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Newton's law of cooling is T = A * e ^ (- d * i) + C_{i} where T is the temperature of the object at time and C is the constant temperature of the surrounding mediumSuppose that the room temperature is 71and the temperature of a cup of coffee is 172 degrees when it is placed on the table. How long will it take for the coffee to cool to 129 degrees for k = 0.0459279 Round your answer to two decimal places

Newtons law of cooling is T A e d i Ci where T is the temperature of the object at time and C is the constant temperature of the surrounding mediumSuppose that class=

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Explanation

[tex]\begin{gathered} T=Ae^{-kt}+C \\ 129=172e^{-0.0459279t}+71 \\ switch\text{ sides} \\ 172e^{\left\{-0.0459279t\right\}}+71=129 \\ 172e^{\left\{-0.0459279t\right\}}=129-71 \\ 172e^{\left\{-0.0459279t\right\}}=58 \\ Divide\text{ both sides by 172} \\ \frac{172e^{-0.0459279t}}{172}=\frac{58}{172} \\ e^{-0.0459279t}=\frac{29}{86} \\ Apply\text{ exponent rules} \\ -0.0459279t=\ln \left(\frac{29}{86}\right) \\ t=-\frac{\ln \left(\frac{29}{86}\right)}{0.0459279} \\ t=23.67\text{ minutes} \end{gathered}[/tex]

Answer: 23.67 minutes

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