Constructing differential equations Quiz

1. The rate of increase of $P$ is proportional to $P$. Which equation models this?

• A. $\frac{dP}{dt}=\frac kP$
• B. $\frac{dP}{dt}=kP$
• C. $\frac{dP}{dt}=kt$
• D. $P=kt$

2. The radius $r$ of a puddle decreases at a rate inversely proportional to $r^{2}$. Which equation models this, with $k>0$?

• A. $\frac{dr}{dt}=kr^{2}$
• B. $\frac{dr}{dt}=-kr^{2}$
• C. $\frac{dr}{dt}=\frac{k}{r^{2}}$
• D. $\frac{dr}{dt}=-\frac{k}{r^{2}}$

3. A moving particle's acceleration is proportional to its velocity $v$ and acts against the motion. Which equation models this, with $k>0$?

• A. $\frac{dv}{dt}=-kv$
• B. $\frac{dv}{dt}=kv$
• C. $\frac{dv}{dt}=-\frac kv$
• D. $v=-kt$

4. Liquid enters a tank at $5$ units per minute and leaves at $kV$ units per minute, where $V$ is the volume. Which equation models $V$?

• A. $\frac{dV}{dt}=5+kV$
• B. $\frac{dV}{dt}=kV-5$
• C. $\frac{dV}{dt}=5-kV$
• D. $\frac{dV}{dt}=-5kV$

5. Demand $D$ falls as price $p$ rises, at a rate proportional to $D$. Which equation models this, with $k>0$?

• A. $\frac{dD}{dp}=kD$
• B. $\frac{dD}{dp}=-kD$
• C. $\frac{dD}{dt}=-kD$
• D. $D=-kp$