Question

when you dive below the surface of the water, the pressure increases. you can feel this in your ears when you dive to the bottom of a deep swimming pool or spring. the function that describes this relationship is $p(d) = 14.5 + \frac{20}{66}d$, where $d$ is the depth in feet below the surface of the water and $p$ is the pressure in pounds per square inch (psi).

what is the pressure at the surface of the water? select the correct units from the second box.
select an answer

at what depth is the pressure exactly double the pressure at the surface of the water? select the correct units from the second box.
select an answer

what is the pressure at a depth of 66 feet?
$p(66) =$ select an answer

what is the pressure at a depth of 198 feet?
$p(198) =$ select an answer

Explanation:

Step1: Find surface pressure (d=0)

Substitute $d=0$ into $P(d)=14.5+\frac{29}{66}d$:
$P(0)=14.5+\frac{29}{66}(0)=14.5$
Units: pounds per square inch (PSI)

Step2: Find depth for double surface pressure

Set $P(d)=2\times14.5=29$, solve for $d$:
$29=14.5+\frac{29}{66}d$
Subtract 14.5: $14.5=\frac{29}{66}d$
Rearrange: $d=14.5\times\frac{66}{29}=33$
Units: feet

Step3: Calculate P(66)

Substitute $d=66$ into $P(d)$:
$P(66)=14.5+\frac{29}{66}(66)=14.5+29=43.5$
Units: pounds per square inch (PSI)

Step4: Calculate P(198)

Substitute $d=198$ into $P(d)$:
$P(198)=14.5+\frac{29}{66}(198)=14.5+29\times3=14.5+87=101.5$
Units: pounds per square inch (PSI)

Answer:

1. Pressure at surface: 14.5, units: pounds per square inch (PSI)
2. Depth for double pressure: 33, units: feet
3. $P(66)=43.5$, units: pounds per square inch (PSI)
4. $P(198)=101.5$, units: pounds per square inch (PSI)