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Answer :
The temperature of the cooling tea can be calculated using an exponential decay formula, resulting in approximately 94.83°F, which, when rounded, is 95°F after 4 minutes. Option c) is correct.
To find the temperature of the tea after 4 minutes, we need to integrate the cooling rate over the period of time we are interested in. However, the provided rate of cooling is a simple exponential decay, and it's more straightforward to use the formula for exponential decay, which is given by:
T(t) = T0 + (Tambient - T0) ∙ (1 - e-kt)
Where T(t) is the temperature of the tea at time t, T0 is the initial temperature of the tea, Tambient is the ambient temperature, k is the decay constant, and t is the time in minutes.
The question gives us T0 = 200°F, Tambient = 70°F, k = 0.053, and we want to know T(t) when t = 4 minutes.
Plugging the values into the formula, we get:
T(4) = 200°F + (70°F - 200°F) ∙ (1 - e-0.053∙4)
Calculating this gives us:
T(4) ≈ 200°F - 130°F ∙ (1 - e-0.212)
T(4) ≈ 200°F - 130°F ∙ 0.809
T(4) ≈ 200°F - 105.17°F
T(4) ≈ 94.83°F (Rounded to the nearest degree 95°F)
Thus, the correct answer would be:
c. Temperature: 95 degrees Fahrenheit
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