Question

a weather balloon was released from the top of a 500-foot-tall building. after 8 seconds, the weather balloons altitude was 620 feet. at 20 seconds, its altitude was 800 feet. what was the rate of change and the initial value of the weather balloon? the rate of change of the weather balloon is 15 ft/s, and the initial value is 620 feet. the rate of change of the weather balloon is 25 ft/s, and the initial value is 620 feet. the rate of change of the weather balloon is 25 ft/s, and the initial value is 500 feet. the rate of change of the weather balloon is 15 ft/s, and the initial value is 500 feet.

Explanation:

Step1: Calculate rate of change

Rate of change (slope) formula: $\frac{y_2 - y_1}{x_2 - x_1}$. Let $x_1 = 8$, $y_1 = 620$; $x_2 = 20$, $y_2 = 800$.
$\frac{800 - 620}{20 - 8} = \frac{180}{12} = 15$ ft/s.

Step2: Identify initial value

Initial value is the altitude at $t = 0$ (released from 500 - foot building), so initial value = 500 feet.

Answer:

The rate of change of the weather balloon is 15 ft/s, and the initial value is 500 feet.