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

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

Transcript text: 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

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.

Step 1: Analyze the Population Increase

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.

Step 2: Determine the Type of Function

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.

Step 3: Conclusion

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