Quiz about Differential Equations

Question 1

An IV administers medication to a patient's bloodstream at a rate of $$3$$ cubic centimeters per hour. At the same time, the patient's organs remove the medication from the patient's bloodstream at a rate proportional to the current volume $${V}$$ of medication in the bloodstream. Which equation describes this relationship?

Accepted Answer

Covalent bond

Answer

$$\frac{d v}{d t}=3-k v$$

Answer

$$\frac{d v}{d t}=-3 k v$$

Answer

$$ \frac{d v}{d t}=3 k-v$$

Answer

$$\frac{d v}{d t}=k-3 v$$

Question 2

A puppy gains weight, $${W}$$, at a rate approximately inversely proportional to its age, $${t}$$, in months. Which equation describes this relationship?

Accepted Answer

Covalent bond

Answer

$$\frac{d w}{d t}=\frac{k}{t}$$

Answer

$$\frac{d w}{d t}=k t$$

Answer

$$\frac{d w}{d t}=k w$$

Answer

$$\frac{d \omega}{d t}=\frac{k}{w} $$

Question 3

The warming or cooling rate of a drink is proportional to the difference between the ambient temperature $$T_a$$ and the current temperature $${T}$$ of the drink. Which equation describes this relationship?

Accepted Answer

Covalent bond

Answer

$$\frac{d T}{d t}=k(T_{a}-T)$$

Answer

$$\frac{d T}{d t}=\frac{k}{T_{a}-T}$$

Answer

$$T(t)=\frac{k}{T_{a}-T,}$$

Answer

$$T(t)=k(T_{a}-T)$$

Question 4

Given that $$h^{\prime}(x)=\frac{2 h(x)}{x \ln (x)}$$. Is $${h}({x})=4 \ln ({x})$$ a solution to the above equation?

Accepted Answer

Covalent bond

Answer

$$No$$

Answer

$$Yes$$

Answer

$$Yes$$

Question 5

Given that $$y^{\prime}=0.5(100-y)$$. Is $${y}=5 e^{-0.5 x}+100$$ a solution to the above equation?

Accepted Answer

Covalent bond

Answer

$$Yes$$

Answer

$$No$$

Answer

$$No$$

Answer

$$No$$

Differential Equations Calculus Maths Problems and Solutions

Many students find Differential Equations for Calculus particularly challenging. Strengthen your concepts and gain confidence for your exams by solving free questions for Differential Equations from for Calculus preparation.