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)	water pressure (psi)
5	17.1
10	19.5
15	21.9
20	24.3
25	26.7

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 linear - relationship

Assume the relationship between depth $d$ (in feet) and water pressure $P$ (in psi) is linear $P = md + b$. Using the points $(0,14.7)$ and $(5,17.1)$:
The slope $m=\frac{17.1 - 14.7}{5-0}=\frac{2.4}{5}=0.48$.
When $d = 0$, $P=b = 14.7$. So the equation is $P=0.48d + 14.7$.

Step2: Solve Part A

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

Set $P = 25$ in the equation $P=0.48d + 14.7$.
$25=0.48d+14.7$.
Subtract 14.7 from both sides: $25 - 14.7=0.48d$, so $10.3 = 0.48d$.
Then $d=\frac{10.3}{0.48}\approx21.46$ ft.

Answer:

Part A: 20.46 psi
Part B: 21.46 ft