The table shows the water pressure p (in pounds per square inch) on a scuba diver at a depth of d feet.
Depth, d
33
66
99
132
Pressure, p
29.4
44.1
58.8
73.5
What is the water pressure at a depth of 58 feet? Round your answer to the nearest tenth.
a
40.5 psi
b
38.6 psi
c
42.7 psi
d
41.3 psi
We can use linear interpolation to estimate the water pressure at a depth of 58 feet.
First, let's calculate the slope of the line passing through the 33ft and 66ft data points:
slope = (44.1 - 29.4) / (66 - 33) = 0.9 psi per foot
Then, using the slope and the 33ft data point, we can calculate the water pressure at a depth of 58ft:
p = 29.4 + 0.9 * (58 - 33) = 46.5 psi
Rounding to the nearest tenth, we get the answer: 46.5 psi ≈ 46.6 psi.
Therefore, the closest answer choice is (c) 42.7 psi.