Comment on Activity 1

All these functions have the value ${\displaystyle 1}$ at ${\displaystyle t=0}$, so the shared point on all three graphs is ${\displaystyle \text{(}0,1\text{)}}$. All three functions decrease to ${\displaystyle 0}$ as ${\displaystyle t}$ increases to infinity. In fact, these properties are shared by all functions of the form

The larger the value of ${\displaystyle k}$, the faster the function decreases, at least until the function values get close to 0.