Question

caleb went into a cave. the light intensity (in candela per square meter, or cd/sq. m) as a function of depth inside the cave (in m) is graphed. what is the approximate average rate at which the light intensity decreases, as caleb goes from a depth of 5 m to a depth of 14 m? choose 1 answer: 330 cd/sq. m per m 390 cd/sq. m per m 420 cd/sq. m per m 480 cd/sq. m per m

Explanation:

Step1: Find the light intensity at \(x = 5\) and \(x = 14\)

From the graph, when \(x = 5\), \(y_1\approx5000\) cd/sq.m. When \(x = 14\), \(y_2\approx1400\) cd/sq.m.

Step2: Use the average - rate - of - change formula

The average rate of change formula is \(\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 5\), \(x_2=14\), \(y_1\approx5000\), \(y_2\approx1400\). Then \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{1400 - 5000}{14 - 5}=\frac{- 3600}{9}=- 400\) (the negative sign indicates a decrease). The magnitude is approximately \(400\) cd/sq.m per m. Closest value to \(400\) among the options is \(390\) cd/sq.m per m.

Answer:

B. \(390\) cd/sq. m per m