Suppose a diver started at 82 feet below the surface and rose in five steps of 15 feet each. Use an integer to describe his new position in relation to the surface water.

depth after n steps: 82-15n

To determine the diver's new position in relation to the surface water, we need to calculate the total change in depth.

Given that the diver starts at 82 feet below the surface and rises in five steps of 15 feet each, we can determine the change by multiplying the number of steps by the distance per step and then adding it to the initial depth.

Number of steps: 5
Distance per step: 15 feet

Change in depth = (Number of steps) x (Distance per step) = 5 x 15 = 75 feet

Now, to determine the diver's new position, we need to add the change in depth to the initial depth:

New position = Initial depth + Change in depth
New position = 82 feet + 75 feet = 157 feet

Therefore, the diver's new position in relation to the surface water is 157 feet below the surface.