Question

problem solving
rate of change

1. the rate of change is constant in the graph.

descent of a skydiver
height after parachute opens (feet)
time (seconds)
a.) what is the rate of change?
b.) explain what the rate of change means.
c.) how fast does the skydiver descend in minutes?
d.) how fast does the skydiver descend in hours?

Explanation:

Step1: Identify two points on the line

Let's take the points (0, 2500) and (60, 1500) from the graph.

Step2: Calculate the rate of change (slope)

The formula for the rate of change (slope $m$) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 0,y_1=2500,x_2 = 60,y_2 = 1500$, we get $m=\frac{1500 - 2500}{60-0}=\frac{- 1000}{60}=-\frac{50}{3}\text{ feet per second}$.

Step3: Explain the rate of change

The negative rate of change means the skydiver's height is decreasing. The value $\frac{50}{3}\text{ feet per second}$ represents the speed at which the skydiver is descending.

Step4: Convert to feet per minute

Since there are 60 seconds in a minute, to convert the rate from feet - per - second to feet - per - minute, we multiply by 60. So, the rate is $-\frac{50}{3}\times60=- 1000\text{ feet per minute}$. The negative sign indicates descent.

Step5: Convert to feet per hour

Since there are 60 minutes in an hour, to convert the rate from feet - per - minute to feet - per - hour, we multiply by 60. So, the rate is $-1000\times60=-60000\text{ feet per hour}$. The negative sign indicates descent.

Answer:

a. $-\frac{50}{3}\text{ feet per second}$
b. The skydiver's height is decreasing at a rate of $\frac{50}{3}$ feet per second.
c. 1000 feet per minute
d. 60000 feet per hour