A cup of coffee cools at a rate proportional to the difference between its temperature $T$ and the surrounding room temperature of $70^\circ\mathrm{F}$. Which differential equation models this situation, where $k0$?

Question

A cup of coffee cools at a rate proportional to the difference between its temperature $T$ and the surrounding room temperature of $70^\circ\mathrm{F}$. Which differential equation models this situation, where $k>0$?

Accepted Answer

A. $\dfrac{dT}{dt} = -k(T-70)$

Answer

$\dfrac{dT}{dt} = -k(T-70)$

Answer

$\dfrac{dT}{dt} = k(T-70)$

Answer

$\dfrac{dT}{dt} = -k(70-T)$

Answer

$\dfrac{dT}{dt} = -kT$

A cup of coffee cools at a rate proportional to the difference between its temperature $T$ and the surrounding room temperature of $70^\circ\mathrm{F}$ . Which differential equation models this situation, where $k>0$ ?

Explanation

Core Concept

Correct Answer

More Unit 7: Differential Equations practice questions

A cup of coffee cools at a rate proportional to the difference between its temperature TTT and the surrounding room temperature of 70∘F70^\circ\mathrm{F}70∘F. Which differential equation models this situation, where k>0k>0k>0?

Explanation

Core Concept

Correct Answer

More Unit 7: Differential Equations practice questions

A cup of coffee cools at a rate proportional to the difference between its temperature $T$ and the surrounding room temperature of $70^\circ\mathrm{F}$ . Which differential equation models this situation, where $k>0$ ?