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A hot bowl of soup cools according to Newton’s law of cooling. Its temperature (in degrees Fahrenheit) at time t is given by T(t) = 66 + 144e-0.04t, where t is given in minutes.What is the temperature of the soup after 10 minutes? Round your answer to the nearest tenth of a degree.

Respuesta :

In order to calculate the temperature after 10 minutes, let's use the value of t = 10 in the function T(t) and calculate the function value:

[tex]\begin{gathered} T(t)=66+144e^{-0.04t}\\ \\ T(10)=66+144e^{-0.04\cdot10}\\ \\ T(10)=66+144e^{-0.4}\\ \\ T(10)=66+96.53\\ \\ T(10)=162.53 \end{gathered}[/tex]

Rounding to the nearest tenth, the temperature is 162.5 °F.

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