These exercises use Newton’s Law of Cooling. Cooling Soup A...

These exercises use Newton’s Law of Cooling. Cooling Soup A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling, so its temperature at time $t$ is given by $$ T(t)=65+145 e^{-0.05 t} $$ where $t$ is measured in minutes and $T$ is measured in $^{\circ} \mathrm{F}$. (a) What is the initial temperature of the soup? (b) What is the temperature after $10 \mathrm{min} ?$ (c) After how long will the temperature be $100^{\circ} \mathrm{F} ?$

These exercises use Newton’s Law of Cooling.
Cooling Soup A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling, so its temperature at time $t$ is given by
$$
T(t)=65+145 e^{-0.05 t}
$$
where $t$ is measured in minutes and $T$ is measured in $^{\circ} \mathrm{F}$.
(a) What is the initial temperature of the soup?
(b) What is the temperature after $10 \mathrm{min} ?$
(c) After how long will the temperature be $100^{\circ} \mathrm{F} ?$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Newton's Law of Cooling

Newton's Law of Cooling describes how the temperature of an object changes over time in relation to the surrounding environment. It states that the rate at which an object cools (or heats up) is proportional to the difference between its current temperature and the ambient temperature.

Exponential Decay

Exponential decay is a process in which a quantity decreases at a rate proportional to its current value. In the context of cooling problems, the temperature difference between the object and the surrounding medium decreases exponentially over time, leading to equations that involve exponential functions.

Initial Conditions

Initial conditions provide the starting values of the variables in a problem, such as the initial temperature at time zero. They are essential for determining the specific solution to differential equations and ensuring the model accurately reflects the real-world scenario being analyzed.

Solving Exponential Equations

Solving exponential equations typically involves isolating the exponential term and then applying logarithmic functions to solve for variables such as time. This technique is crucial when determining the time required for an object to cool to a specific temperature according to an exponential decay model.

Please give Ace some feedback