Question

A cup of coffee has a temperature of 200F. It is placed in a
room that has temperature 70 F. After 15 minutes, the temperature
of the coffee is 150F.

a) Model the temperature of the cup of coffee at time t.

b) How long will it take for the coffee to cool down to 100◦
F?

Answer #1

If a cup of coffee has temperature 100°C in a room where the
ambient air temperature is 21°C, then, according to Newton's Law of
Cooling, the temperature of the coffee after t minutes is T ( t ) =
21 + 79 e − t / 45 . What is the average temperature of the coffee
during the first 14 minutes?

A 210 degree cup of coffee is placed on a table in a
climate-controlled room with the temperature set at a constant 73
degrees. After 6 minutes, the temperature of the coffee had dropped
to 150 degrees. Find a function that outputs the temperature of the
coffee t minutes after it is placed on the table.

The temperature, T, of a cup of tea is modelled by the
function T = 21 + 58.8(1.4)-x ,where T is measured in 0C (degrees
Celsius) and x is measured in minutes. The time starts to be
measured when the tea is poured into the cup.
1) Graph the function using
technology. Include a graph in your response.
2) Find the temperature of the tea in the cup in 0C
and 0F:
a) when the tea is poured into...

In 1701, Issac Newton proved his Law of Cooling: T(t)
=Aekt +Ta, which is an exponential model that
relates the temperature of an object T as a function of
time t (we will use minutes) that is placed in an
environment with ambient temperature Ta.
Suppose a cup of hot coffee is served at 160◦F and placed in a
room with an ambient temperature 75◦. After 5 minutes, the cup of
coffee has a temperature of 131◦F.
a) Create a...

A cup of tea is cooling in a room that has a constant
temperature of 70 degrees Fahrenheit (F). If the initial
temperature of the tea, at time t=0 minutes, is 200 F and the
temperature of the tea changes at the rate: R(t) -6.89e^(-.053t)
degrees Fahrenheit per minute, what is the temperature, to the
nearest degree, of the tea after 4 minutes? 2. On the closed
interval [2, 4], which of the following could be the graph of a...

According to Newton's Law of Cooling
A cup of coffee with temperature of 130F is placed in a freezer
with temperature 0F. After 5 minutes, the temperature of the coffee
is 87F. Find the coffee's temperature
after 10 minutes.

Suppose a cup of coffee is at 100 degrees Celsius at time t=0,
it is at 70 degrees at t=15 minutes, and it is at 45 degrees at
t=30 minutes. Compute the ambient temperature.

A mug of coffee, with a temperature ?℃ is made and left to cool
in a room with a temperature of 25℃. The rate at which the coffee
cools is proportional to the difference in temperature between the
coffee and the room. Initially the coffee is at a temperature 85℃.
10 minutes later the coffee is at 55℃. Determine the temperature,
to 1 decimal place, of the coffee after 15 minutes.

Suppose that a cup of soup cooled from 90C to 50C after 25
minutes in a room whose temperature was 20C. Use Newton's law of
cooling to answer the following questions.
a. How much longer would it take the soup to cool to 30C? (in
minutes)
b. Instead of being left to stand in the room, the cup of 90C
soup is put in the freezer whose temperature is -15C. How long will
it take the soup to cool from...

A covered mug of coffee originally at 190 degrees Fahrenheit, if
left for t hours in a room whose temperature is 60
degrees, will cool to a temperature of
60 +
130e−1.7t
degrees. Find the temperature of the coffee after the following
amounts of time. (Round your answers to the nearest degree.)
(a) 15 minutes
°F
(b) half an hour
°F

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