A baker records the internal temperature of a pie that has been left out on the counter. The room temperature is 14 Celsius. An equation that models this situation is T (t) = 68 (0.5) ^r/10 where T is the temperature in degrees Celsius and t is the time in minutes. Determine the temperature to the nearest degree, of the pie after 15

minutes. How much time did it take for the pie to reach an internal temperature of 31°C?

Question

Mathematics

Opie

14 January, 08:18

A baker records the internal temperature of a pie that has been left out on the counter. The room temperature is 14 Celsius. An equation that models this situation is T (t) = 68 (0.5) ^r/10 where T is the temperature in degrees Celsius and t is the time in minutes. Determine the temperature to the nearest degree, of the pie after 15

minutes. How much time did it take for the pie to reach an internal temperature of 31°C?

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Jewel Bridges · Answer 1

Assume r = t not sure if you mistyped this.

t = 15 min

T (t) = 68 (0.5) ^ (15/10) = 24 Celsius

31 = (0.5) ^ (t/10) take ln

ln31 = (t/10) ln (0.5) + ln68

t = (ln32 - ln 68/ln0.5) * 10 = 11.3 min