Is $y=3e^{-5x}$ a solution of $\frac{dy}{dx}=-5y$?

Is $y=6e^{-5x}$ a solution of $\frac{dy}{dx}=-5y$?

A room warms so that its temperature $T$ changes at a rate proportional to the DIFFERENCE between $T$ and the surrounding temperature $21^{\circ }\text{C}$, with constant $k$ and $t$ in minutes. Which equation says this?

The balance of an account, $B$, changes at a rate proportional to $B$, with constant of proportionality $k$ and $t$ in years. Which differential equation says this?

Which function satisfies $\frac{dy}{dx}=3y$?

Which function satisfies $\frac{dy}{dx}=4y$?

Is $y=8e^{4x}$ a solution of $\frac{dy}{dx}=3y$?

A colony's population, $P$, changes at a rate proportional to the SQUARE of $P$, with constant of proportionality $k$ and $t$ in hours. Which differential equation says this?

The mass of a radioactive sample, $M$, changes at a rate proportional to the SQUARE ROOT of $M$, with constant of proportionality $k$ and $t$ in years. Which differential equation says this?

Is $y=9e^{-3x}$ a solution of $\frac{dy}{dx}=-3y$?

A cup of coffee cools so that its temperature $T$ changes at a rate proportional to the DIFFERENCE between $T$ and the surrounding temperature $68^{\circ }\text{F}$, with constant $k$ and $t$ in minutes. Which equation says this?

Is $y=2e^{-6x}$ a solution of $\frac{dy}{dx}=-5y$?

The volume of water in a tank, $V$, changes at a rate proportional to the SQUARE of $V$, with constant of proportionality $k$ and $t$ in minutes. Which differential equation says this?

Which function is a solution of $y^{\prime \prime }+25y=0$?

The balance of an account, $B$, changes at a rate INVERSELY proportional to $B$, with constant of proportionality $k$ and $t$ in years. Which differential equation says this?

A can of soda warms so that its temperature $T$ changes at a rate proportional to the DIFFERENCE between $T$ and the surrounding temperature $75^{\circ }\text{F}$, with constant $k$ and $t$ in minutes. Which equation says this?

Is $y=3e^{4x}$ a solution of $\frac{dy}{dx}=3y$?

The volume of water in a tank, $V$, changes at a rate proportional to the SQUARE ROOT of $V$, with constant of proportionality $k$ and $t$ in minutes. Which differential equation says this?

A pie cools on a rack so that its temperature $T$ changes at a rate proportional to the DIFFERENCE between $T$ and the surrounding temperature $72^{\circ }\text{F}$, with constant $k$ and $t$ in minutes. Which equation says this?

Which function satisfies $\frac{dy}{dx}=5y$?

Is $y=4e^{6x}$ a solution of $\frac{dy}{dx}=5y$?

The balance of an account, $B$, changes at a rate proportional to the SQUARE ROOT of $B$, with constant of proportionality $k$ and $t$ in years. Which differential equation says this?

Is $y=4e^{2x}$ a solution of $\frac{dy}{dx}=2y$?

Which function satisfies $\frac{dy}{dx}=-3y$?