Question

water pressure
the water pressure at different depths in a swimming pool is
measured and recorded in the table. use the data provided in the
table to answer the questions.
part a
what is the water pressure at a depth of 12 feet? (round to the
nearest hundredth)
psi
part b
at what depth does the water pressure reach 25 psi? (round to
the nearest hundredth)
ft

Explanation:

Step1: Find the rate of change (slope)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(x\) be depth (feet) and \(y\) be water pressure (psi). Using \((x_1,y_1)=(0,14.7)\) and \((x_2,y_2)=(5,17.1)\)

$$m=\frac{17.1 - 14.7}{5-0}=\frac{2.4}{5}=0.48$$

The equation of the line in slope - intercept form \(y = mx + b\). Since \(b = 14.7\) (when \(x = 0\)), the equation is \(y=0.48x + 14.7\)

Step2: Solve Part A

For \(x = 12\), substitute into \(y=0.48x + 14.7\)

$$y=0.48\times12+14.7=5.76 + 14.7=20.58$$

Step3: Solve Part B

Set \(y = 25\) in \(y=0.48x + 14.7\)

$$25=0.48x+14.7$$

$$0.48x=25 - 14.7$$

$$0.48x=10.3$$

$$x=\frac{10.3}{0.48}\approx41.67$$

Answer:

Part A

$20.58$ psi

Part B

$41.67$ ft