Question

els the data.
2.
j | k
0 | 3
5 | 28
10 | 53
15 | 78
20 | 103
av/δx = 25/5 = 5

Explanation:

Step1: Identify Δk and Δj

To find the average rate of change, we use two points. Let's take the first point (j₁, k₁) = (0, 3) and the last point (j₂, k₂) = (20, 103). Then, Δk = k₂ - k₁ = 103 - 3 = 100, and Δj = j₂ - j₁ = 20 - 0 = 20. But looking at the table, the change in j (Δx) between consecutive rows: from 0 to 5, Δj = 5 - 0 = 5; 5 to 10, Δj = 5; etc. The change in k (Δk) between consecutive rows: 28 - 3 = 25; 53 - 28 = 25; 78 - 53 = 25; 103 - 78 = 25. So for each interval, Δk = 25 and Δj = 5.

Step2: Calculate Average Rate of Change

The formula for average rate of change is $\frac{\Delta k}{\Delta j}$. Using Δk = 25 and Δj = 5 (for one interval, but since it's constant, it's the same for all). So $\frac{25}{5} = 5$.

Answer:

The average rate of change $\frac{\Delta k}{\Delta j}$ is 5.