Answer: The diver's new depth is 11.8 feet below the water's surface.
Step-by-step explanation:
Since we have given that
Depth below the water's surface = 15 feet
The diver swims up slowly at 0.5 feet per second for 4 seconds.
Number of miles he swims up is given by

Number of miles he swims up for 3 more seconds at 0.4 feet per second.
So, Number of miles he swims up is given by

So, the diver's new depth would be

Hence, the diver's new depth is 11.8 feet below the water's surface.