Question

kayla takes hot air balloon a, and umar takes hot air balloon b. after 2 seconds, kayla was 52 feet in the air, and after 5 seconds, she was 35 feet in the air. after 1 second, umar was 50 feet in the air, and after 4 seconds, he was 32 feet in the air. who was descending at a faster rate? kayla: (2, 52) and (5, 35) umar: (1, 50) and (4, 32) kaylas rate of change is (square). that means that her height in the air decreases (square) feet every second. umars rate of change is (square). that means that his height in the air decreases (square) feet every second.

Explanation:

Step1: Calculate Mila's rate of change

The rate of change formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For Mila, \(x_1 = 2,y_1 = 52,x_2 = 5,y_2 = 35\).

$$m=\frac{35 - 52}{5 - 2}=\frac{-17}{3}\approx - 5.67$$

This means her height in the air decreases about \(5.67\) feet every second.

Step2: Calculate Umar's rate of change

For Umar, \(x_1 = 1,y_1 = 50,x_2 = 4,y_2 = 32\).

$$m=\frac{32 - 50}{4 - 1}=\frac{-18}{3}=-6$$

This means his height in the air decreases \(6\) feet every second.

Answer:

Mila's rate of change is \(-\frac{17}{3}\approx - 5.67\). That means her height in the air decreases about \(5.67\) feet every second.
Umar's rate of change is \(-6\). That means his height in the air decreases \(6\) feet every second.