Question

manco went scuba diving. as he dove deeper, the water pressure around him increased at a constant rate.
the table compares mancos depth (in meters) and the water pressure around him (in atmospheres).
depth (meters) pressure (atmospheres)
14 2.4
18 2.8
22 3.2
what was the pressure around manco when he was 30 meters deep?
_____ atmospheres

Explanation:

Step1: Find pressure rate per meter

First, calculate the change in pressure over change in depth. Using the first two data points:
$\text{Rate} = \frac{2.8 - 2.4}{18 - 14} = \frac{0.4}{4} = 0.1$ atmospheres per meter.

Step2: Define linear pressure formula

The relationship is linear, so use $P = P_0 + 0.1d$, where $P$ is pressure, $d$ is depth, and $P_0$ is surface pressure. Solve for $P_0$ using $d=14$, $P=2.4$:
$2.4 = P_0 + 0.1(14)$
$P_0 = 2.4 - 1.4 = 1.0$
The formula is $P = 1 + 0.1d$.

Step3: Calculate pressure at 30m

Substitute $d=30$ into the formula:
$P = 1 + 0.1(30)$
$P = 1 + 3 = 4.0$

Answer:

4.0 atmospheres