Questions: Determine whether the following statement represent an exponential function or a linear function. The average annual population of a pack of wolves increases each year by 25 wolves. exponential linear

Solution Steps

To determine whether the given statement represents an exponential function or a linear function, we need to analyze the nature of the increase in the population. If the population increases by a constant number each year, it is a linear function. If the population increases by a constant percentage each year, it is an exponential function. In this case, the population increases by a constant number (25 wolves) each year, which indicates a linear function.

The problem states that the average annual population of a pack of wolves increases by $25$ wolves each year. This indicates that the increase is a constant value rather than a percentage of the current population.

Since the population increases by a constant number, we can express this mathematically as: $$P(t) = P_0 + 25t$$ where $P(t)$ is the population at time $t$, $P_0$ is the initial population, and $t$ is the number of years. This equation represents a linear function.

Given that the increase is by a constant number, we conclude that the function representing the population of the wolves is linear.

Final Answer