Here is the graph of the function $N(t) = \frac{778}{1 + 5e^{-0.02t}}$. It shows how $N$ changes over time, approaching a limiting value as $t$ increases.

Would you like more details on this function, such as its properties or asymptotic behavior?

Here are some related questions for further exploration:

1. What is the long-term behavior of the function as $t$ approaches infinity?
2. How does the value of $k$ affect the shape and asymptote of the graph?
3. Can we find the initial growth rate of $N$ when $t = 0$?
4. How does modifying the constant $r$ change the growth rate?
5. How would the function change if the exponent's sign were reversed?

Tip: The horizontal asymptote of such logistic-like functions can often be found by evaluating the function as $t$ goes to infinity.