Answer:
The dolphin is five feet in the air after about 0.22 and 1.40 seconds.
Step-by-step explanation:
The height <em>h</em> (in feet) of the dolphin as it jumped out of the water after <em>t</em> seconds is given by the function:
We want to determine the time(s) when the dolphin is five feet in the air.
Since the dolphin is five feet in the air, h(t) = 5:
Solve for t. Rearrange:
We can use the quadratic formula, given by:
In this case, a = 16, b = -26, and c = 5.
Substitute:
Evaluate:
Simplify the square root:
Hence:
Simplify:
Hence, our solutions are:
The dolphin is five feet in the air after about 0.22 and 1.40 seconds.