Question

Larry tossed a coin off of a bridge. The path of the coin can be modeled by the function y = -16t^2 + 72t + 100, where t is the time in seconds and h is the height in feet. If we want to analyze the coin's motion in the time interval from t = -1 to t = 8 seconds, what is the range of heights (y-values) we should consider for this analysis?

A. -2 to 220 feet
B. 0 to 100 feet
C. -100 to 72 feet
D. 8 to 100 feet

Answer 1

The range of heights for the given function in the time interval from t = -1 to t = 8 seconds is from -348 to 12 feet.

Step-by-step explanation:

The given function is y = -16t^2 + 72t + 100. We need to find the range of heights (y-values) in the time interval from t = -1 to t = 8 seconds.

To determine the range, we substitute the given time values into the function to find the corresponding heights.

y(-1) = -16(-1)^2 + 72(-1) + 100 = -16 + (-72) + 100 = 12 feet.

y(8) = -16(8)^2 + 72(8) + 100 = -1024 + 576 + 100 = -348 feet.

Therefore, the range of heights we should consider for this analysis is from -348 to 12 feet. Option C (-100 to 72 feet) is the closest range to this result.