Let's break down the question step-by-step:
1. What does [tex]\( t \)[/tex] represent?
[tex]\( t \)[/tex] represents the time in years since 2008. This is important because it helps us understand how far into the future (from the year 2008) we are measuring the population of bobcats.
- Answer: [tex]\( t \)[/tex] represents time in years since 2008.
2. What is the domain for this function?
The domain of the function refers to all possible values of [tex]\( t \)[/tex] that we can input into the function. Since [tex]\( t \)[/tex] measures time in years since 2008, it starts from the year 2008 onwards. Hence, [tex]\( t \)[/tex] can be 0 (representing the year 2008) and continue indefinitely into the future.
- Answer: The domain is [tex]\([0, +\infty)\)[/tex].
3. Which range values would not make sense for this function?
The range of the function includes all possible values of the population of bobcats that the function can output. In this context, since we are talking about a population, it would not make sense for the population values to be negative. Negative population values are not realistic in this context.
- Answer: Negative population values would not make sense.
4. Would the graph be continuous or discrete, and why?
The graph of the function would be continuous because both time and population can be measured continuously. Time flows without interruption, and population can vary in a smooth manner rather than jumping from one value to another abruptly.
- Answer: The graph would be continuous, because time and population are measured continuously.
By understanding these aspects, we get a clearer picture of how the function models the population of bobcats over time since 2008, realizing that we are dealing with a continuous model starting from the year 2008 and extending indefinitely into the future, with the population always being non-negative.
