Question

1. the table models the height of a remote - control helicopter over 20 seconds during flight. determine the average rate of change in height during the interval of 10 seconds to 15 seconds. interpret the rate in context.

Explanation:

Step1: Recall the formula for average rate of change

The formula for average rate of change is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x$ represents time (in seconds) and $y$ represents height (in feet). For the interval from $x_1 = 10$ seconds to $x_2=15$ seconds, $y_1 = 20$ feet and $y_2 = 14$ feet.

Step2: Substitute the values into the formula

Substitute $x_1 = 10$, $y_1 = 20$, $x_2 = 15$, and $y_2 = 14$ into the formula:
$$\frac{y_2 - y_1}{x_2 - x_1}=\frac{14 - 20}{15 - 10}$$

Step3: Calculate the numerator and denominator

Calculate the numerator: $14-20=-6$. Calculate the denominator: $15 - 10 = 5$. So, $\frac{-6}{5}=-1.2$.

Answer:

The average rate of change is $- 1.2$ feet per second. This means that, on average, the height of the remote - control helicopter is decreasing at a rate of $1.2$ feet per second during the interval from $10$ seconds to $15$ seconds.