Question

determine the value of the given term, and explain what it means. the local wolf population is declining. the graph shows the local wolf population over time. find f(8) and explain what it represents.

Explanation:

Step1: Identify the pattern of population decline

By observing the points \((1,110)\), \((2,101)\), \((3,92)\), \((4,83)\), \((5,74)\), we can see that the population of wolves is decreasing by 9 each week. The general formula for a linear - decreasing function is \(y = mx + b\), where \(m=- 9\) (the rate of change). Using the point - slope form with the point \((1,110)\): \(y - 110=-9(x - 1)\), which simplifies to \(y=-9x + 119\).

Step2: Calculate \(f(8)\)

Substitute \(x = 8\) into the function \(y=-9x + 119\). So \(y=-9\times8 + 119\). First, calculate \(-9\times8=-72\). Then, \(-72 + 119 = 47\).

Answer:

1. It represents the number of wolves in the local population after 8 weeks, assuming the observed pattern of decline continues.