Pls me on this math question. i am really confused

640 m

Step-by-step explanation:

We can consider 4 seconds to be 1 time unit. Then 8 more seconds is 2 more time units, for a total of 3 time units.

The distance is proportional to the square of the number of time units. After 1 time unit, the distance is 1² × 80 m. Then after 3 time units, the distance will be 3² × 80 m = 720 m.

In the additional 2 time units (8 seconds), the ball dropped an additional

... (720 -80) m = 640 m

Alternate solution

You can write the equation for the proportionality and find the constant that goes into it. If we use seconds (not 4-second intervals) as the time unit, then we can say ...

... d = kt²

Filling in the information related to the first 4 seconds, we have ...

... 80 = k(4)²

... 80/16 = k = 5

Then the distance equation becomes ...

... d = 5t²

After 12 seconds (the first 4 plus the next 8), the distance will be ...

... d = 5×12² = 5×144 = 720 . . . meters

That is, the ball dropped an additional 720 -80 = 640 meters in the 12 -4 = 8 seconds after the first data point.