Question

average rate of change quick check
a helium balloon is at a height of 1,200 ft. after two minutes in flight. the balloon finally pops after seven minutes in flight, at a height of 10,500 ft. what is the average rate of change in height for the balloon over this period of time? (1 point)
1,860.00 ft./min
1,860 ft./min
1,860 ft./min
1,860 ft./min

Explanation:

Step1: Identify the formula for average rate of change

The formula for average rate of change is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y$ represents height and $x$ represents time.

Step2: Assign values to variables

Let $x_1 = 2$ minutes, $y_1=1200$ ft, $x_2 = 7$ minutes, and $y_2 = 10500$ ft.

Step3: Substitute values into the formula

$\frac{y_2 - y_1}{x_2 - x_1}=\frac{10500 - 1200}{7 - 2}$.
First, calculate the numerator: $10500-1200 = 9300$.
Then, calculate the denominator: $7 - 2=5$.

Step4: Calculate the final result

$\frac{9300}{5}=1860$ ft/min.

Answer:

$1860$ ft/min.