Answer:
Refer below
Step-by-step breakdown:
The function behaves as a piecewise function defined as:

a)
We need to evaluate the limit of the function as t approaches infinity. This means determining the maximum number of fish present in the pond as time extends indefinitely.
We consider the second segment of the equation since t fits into that range, whereby t is infinite, clearly exceeding 8.

This indicates that the maximum fish population in this pond is 1600, regardless of the time.
b)
A function is considered continuous at a specific point if the limit and the function value at that point are the same.
The function value at t = 8, according to the second part of the equation, is:

We observe that a value exists, and the limit approaches this as t nears 8.
<pthus>the function maintains continuity at t = 8
c)
We seek to determine if there exists a "time" during t from 0 to 6 when the fish count in the pond reaches 250. Substituting 250 into N(t) allows us to solve for t using the first portion of the piecewise function as shown below:

The time is 4 years when the fish count in the pond becomes 250
</pthus>