Isaac Newton is credited for discovering the fact that objects cool at a rate proportional to the difference in the object's temperature and its surroundings. The function that models this is: T (t) = Ts + (To – Ts)et %3D - T (t) is the object's temperature after t minutes To is the object's initial temperature Ts is the temperature of the object's surroundings (ambient temperature) r is the cooling factor (similar to a rate) Problem: A 192 °F cup of coffee is set into a 63 °F room. After 20 minutes, the coffee is found to be 139 °F. Find To, Ts, and r then complete the given formula for the temperature of the coffee as a function of time: (use as many decimal places for r as possible) Number T(t) = Number +( Number Number Je %3D Estimate the temperature of the cup of coffee after a total of 30 minutes. Number °F (round to one decimal place)
Isaac Newton is credited for discovering the fact that objects cool at a rate proportional to the difference in the object's temperature and its surroundings. The function that models this is: T (t) = Ts + (To – Ts)et %3D - T (t) is the object's temperature after t minutes To is the object's initial temperature Ts is the temperature of the object's surroundings (ambient temperature) r is the cooling factor (similar to a rate) Problem: A 192 °F cup of coffee is set into a 63 °F room. After 20 minutes, the coffee is found to be 139 °F. Find To, Ts, and r then complete the given formula for the temperature of the coffee as a function of time: (use as many decimal places for r as possible) Number T(t) = Number +( Number Number Je %3D Estimate the temperature of the cup of coffee after a total of 30 minutes. Number °F (round to one decimal place)
Chapter3: Functions
Section3.2: Domain And Range
Problem 61SE: The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is...
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Transcribed Image Text:Isaac Newton is credited for discovering the fact that objects cool at a rate proportional to the
difference in the object's temperature and its surroundings.
The function that models this is: T (t) = Ts+ (To – Ts)et
T (t) is the object's temperature after t minutes
To is the object's initial temperature
Ts is the temperature of the object's surroundings (ambient temperature)
r is the cooling factor (similar to a rate)
Problem: A 192 °F cup of coffee is set into a 63 °F room. After 20 minutes, the coffee is found to be
139 °F.
Find To, Ts, and r then complete the given formula for the temperature of the coffee as a function of
time:
(use as many decimal places for r as possible)
Number
T(t) = Number
+( Number
Number
Je
%3D
Estimate the temperature of the cup of coffee after a total of 30 minutes.
Number
°F (round to one decimal place)
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