Question

1. which graph has the greater rate of change?

(graph with two lines labeled bank a (blue) and bank b (red) on a coordinate grid, starting at (0, 40) and decreasing)

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Both graphs start at \((0, 40)\) (y - intercept). Let's find another point for each. Assume for Park B, when \(x\) is some value, \(y\) is lower, and for Park A, same. But visually, Park B's line is steeper (more negative, but magnitude). Let's take end points. Suppose Park B ends at \((x_B, 0)\) and Park A at \((x_A, 0)\). From graph, Park B reaches 0 faster (shorter \(x\) - distance). Let's pick two points for each:

For Park B: \((0, 40)\) and say \((4, 0)\) (approx, since it's steeper). Rate of change \(m_B=\frac{0 - 40}{4 - 0}=\frac{- 40}{4}=- 10\).

For Park A: \((0, 40)\) and say \((6, 0)\) (since it's less steep). Rate of change \(m_A=\frac{0 - 40}{6 - 0}=\frac{- 40}{6}\approx - 6.67\).

The magnitude of rate of change for Park B (\(|-10| = 10\)) is greater than Park A (\(|-6.67|\approx6.67\)). So Park B has greater rate of change (more negative, but in terms of magnitude of change).

Step2: Compare magnitudes

Since we care about "greater rate of change" (magnitude, as rate of change can be negative, but the question is about which changes faster). The steeper line (Park B) has a greater absolute rate of change.

Answer:

Park B