Question

question 14 of 24
look at the graph and extrapolate how many baskets were made by the team at 8.5 minutes.
cumulative number of basket balls
time (min)

Explanation:

Step1: Observe the graph trend

The graph shows the cumulative number of basket - balls made over time. After 8 minutes, the number of baskets is around 25 and then it drops to 5 at 10 minutes. We assume a linear decrease between 8 and 10 minutes.

Step2: Calculate the rate of change

The change in the number of baskets from 8 minutes to 10 minutes is $5 - 25=- 20$. The change in time is $10 - 8 = 2$ minutes. So the rate of change is $\frac{5 - 25}{10 - 8}=\frac{-20}{2}=-10$ baskets per minute.

Step3: Extrapolate for 8.5 minutes

We use the point - slope form. Let $x$ be the time and $y$ be the number of baskets. We know at $x = 8$, $y = 25$ and the slope $m=-10$. The equation of the line for the decrease is $y - y_1=m(x - x_1)$. For $x = 8.5$, we have $y-25=-10(8.5 - 8)$. Then $y-25=-10\times0.5$, $y-25=-5$, $y = 20$. But looking at the graph and making a rough estimate, since the decrease starts after 8 minutes and is not a perfect linear model before that, we can also estimate by eye - balling. The number of baskets at 8.5 minutes is closest to 15.

Answer:

C. 15