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?

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...

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 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

A cup of coffee at 90 Celsius is put into a 20 Celsius room,
t=0. The coffee's temperature is changing at a rate of r (t) =
-7(0.7^t) Celsius per minute, with t in minutes. Estimate the
coffees temperature when t=10.
Round answer to TWO decimal places:

A student brings a cup of hot (190° ) coffee to her evening
Differential Equations course. Unfortunately, the classroom is 80°
that day because the air conditioner is broken. Ms. Jensen opens
the door and the classroom begins to cool at a constant rate of 10°
per hour. The student is so absorbed in the class that she forgets
about her coffee and it sits on her desk for 50 minutes as the
classroom cools down. In this problem the...

Newton's Law of Cooling tells us that the rate of change of the
temperature of an object is proportional to the temperature
difference between the object and its surroundings. This can be
modeled by the differential equation dTdt=k(T−A)dTdt=k(T-A), where
TT is the temperature of the object after tt units of time have
passed, AA is the ambient temperature of the object's surroundings,
and kk is a constant of proportionality.
Suppose that a cup of coffee begins at 179179 degrees and,...

The oven was at room temperature 70℉. Just after it was turned
on, the temperature rose 40℉ per minute. What does the independent
variable represent? What does the dependent variable represent?
Graph your results. Be sure to graph the independent variable on
the horizontal axis. What will the temperature of the oven be after
6 minutes? Write an algebraic model (equation) for this
application. How long will it take before the temperature is
450℉.

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