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.
depth (feet)
0 5 10 15 20 25
water pressure (psi)
14.7 17.1 19.5 21.9 24.3 26.7
part a
what is the water pressure at a depth of 12 feet? (round to the nearest hundredth)
part b
at what depth does the water pressure reach 25 psi? (round to the nearest hundredth)

Explanation:

Step1: Assume a linear - relationship between depth $d$ and pressure $P$.

Let the linear equation be $P = md + b$, where $m$ is the slope and $b$ is the y - intercept. Using the points $(d_1,P_1)=(0,14.7)$ and $(d_2,P_2)=(5,17.1)$:
The slope $m=\frac{P_2 - P_1}{d_2 - d_1}=\frac{17.1 - 14.7}{5-0}=\frac{2.4}{5}=0.48$.
Since when $d = 0$, $P = 14.7$, then $b = 14.7$. So the equation is $P=0.48d + 14.7$.

Step2: Solve Part A.

We want to find $P$ when $d = 12$. Substitute $d = 12$ into the equation $P=0.48d + 14.7$.
$P=0.48\times12 + 14.7=5.76+14.7 = 20.46$ psi.

Step3: Solve Part B.

We want to find $d$ when $P = 25$. Substitute $P = 25$ into the equation $P=0.48d + 14.7$.
$25=0.48d+14.7$.
First, subtract 14.7 from both sides: $25 - 14.7=0.48d$, so $10.3 = 0.48d$.
Then, solve for $d$: $d=\frac{10.3}{0.48}\approx21.46$ ft.

Answer:

Part A: 20.46 psi
Part B: 21.46 ft