A radioactive sample decays continuously with a half-life of $4$ days. What is $k$ in $y=y_0{e}^{kt}$, with $t$ in days?

A radioactive sample decays continuously with a half-life of $15$ years. What is $k$ in $y=y_0{e}^{kt}$, with $t$ in years?

A radioactive sample decays continuously with a half-life of $24$ days. What is $k$ in $y=y_0{e}^{kt}$, with $t$ in days?

The amount in a bacteria culture satisfies $\frac{dy}{dt}=0.03y$ with $y(0)=200$ and $t$ in hours. Which is $y(t)$?

A bacteria culture grows continuously and doubles every $5$ hours. If it starts at $800$ cells, how many cells are there after $20$ hours?

The concentration of a drug in the blood satisfies $\frac{dy}{dt}=-0.06y$ with $y(0)=100$ and $t$ in hours. Which is $y(t)$?

The concentration of a drug in the blood satisfies $\frac{dy}{dt}=-0.08y$ with $y(0)=100$ and $t$ in hours. Which is $y(t)$?

A bacteria culture grows continuously and doubles every $3$ hours. If it starts at $1000$ cells, how many cells are there after $9$ hours?

An object at $40^{\circ }\text{F}$ is placed in surroundings at $68^{\circ }\text{F}$ and satisfies $\frac{dT}{dt}=-0.04\left(T-68\right)$, with $t$ in minutes. Which is $T(t)$?

The amount in a bacteria culture satisfies $\frac{dy}{dt}=0.03y$ with $y(0)=500$ and $t$ in hours. Which is $y(t)$?

In the model $P=P_0{e}^{kt}$ for a town's population, with $t$ in hours, $k=0.008$. What does this say?

An object at $200^{\circ }\text{F}$ is placed in surroundings at $72^{\circ }\text{F}$ and satisfies $\frac{dT}{dt}=-0.03\left(T-72\right)$, with $t$ in minutes. Which is $T(t)$?

An object at $40^{\circ }\text{C}$ is placed in surroundings at $20^{\circ }\text{C}$ and satisfies $\frac{dT}{dt}=-0.1\left(T-20\right)$, with $t$ in seconds. Which is $T(t)$?

In the model $P=P_0{e}^{kt}$ for a town's population, with $t$ in hours, $k=-0.012$. What does this say?

The amount in a bacteria culture satisfies $\frac{dy}{dt}=0.08y$ with $y(0)=150$ and $t$ in hours. Which is $y(t)$?

A bacteria culture grows continuously and doubles every $5$ hours. If it starts at $500$ cells, how many cells are there after $20$ hours?

In the model $P=P_0{e}^{kt}$ for a town's population, with $t$ in hours, $k=-0.031$. What does this say?

A bacteria culture grows continuously and doubles every $3$ hours. If it starts at $800$ cells, how many cells are there after $12$ hours?

An object at $110^{\circ }\text{F}$ is placed in surroundings at $72^{\circ }\text{F}$ and satisfies $\frac{dT}{dt}=-0.04\left(T-72\right)$, with $t$ in minutes. Which is $T(t)$?

A bacteria culture grows continuously and doubles every $6$ hours. If it starts at $300$ cells, how many cells are there after $18$ hours?

A radioactive sample decays continuously with a half-life of $4$ years. What is $k$ in $y=y_0{e}^{kt}$, with $t$ in years?

A radioactive sample decays continuously with a half-life of $5$ hours. What is $k$ in $y=y_0{e}^{kt}$, with $t$ in hours?

In the model $P=P_0{e}^{kt}$ for a town's population, with $t$ in hours, $k=0.045$. What does this say?

A bacteria culture grows continuously and doubles every $3$ hours. If it starts at $800$ cells, how many cells are there after $9$ hours?