Computing the Time to Bake Potatoes An oven is preheated and then remains at a c
ID: 3629848 • Letter: C
Question
Computing the Time to Bake Potatoes
An oven is preheated and then remains at a constant temperature. A potato is placed in the oven to bake. Food scientists have measured the rise of temperature of a baking potato. They have found that the temperature T (in degrees Fahrenheit) of the potato can be described by the relation given by the equation
where t is the amount of time (in minutes) after the potato is put in the oven.
T = 420-345*.95^t
The potato will be considered done when its temperature is anywhere between 260 and 280 degrees Fahrenheit.
(a) Enter two numbers that are the start and end times of "doneness". Enter a number with decimal point.
Doneness begins at t = minutes after the potato is put into the oven.
Doneness ends at t = minutes after the potato is put into the oven.
(b) How long does it take for the difference between the potato's starting temperature and the oven's temperature to be cut in half?
It takes approximately_____minutes for the potato's temperature to get half way from its starting temperature to the oven's temperature.
Explanation / Answer
(a) asks to solve for t, the time, with a given T.
So, rearranging...
log((420 - T)/ 345) / log(.95) = t
Plugging in T = 260 and T = 280,
Doneness begins at t = 14.97994252 minutes after the potato is put into the oven.
Doneness ends at t = 17.58323393 minutes after the potato is put into the oven.
(b) Plug in t=0 into the original equation to find T, the potato's starting temperature.
Potato's starting temperature = 75
The oven's temperature is 420.
So, half the difference is (420 - 75) / 2 = 172.5.
Therefore, plug in 172.5 into T in the equation from (a).
It takes approximately 6.475190159 minutes for the potato's temperature to get half way from its starting temperature to the oven's temperature.
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