(1 pt) At the surface of the ocean, the water pressure is the same as the air pressure above the water, about 15lb/in2, Below the surface the water pressure increases by about 4.24lb/in2 for every 10 ft of descent.

Write a function f(x) which expresses the water pressure in pounds per square inch as a function of the depth in inches below the ocean surface.

f(x) = 15 + 4.24(x/120)

To write the function f(x) that expresses the water pressure in pounds per square inch (lb/in^2) as a function of the depth in inches below the ocean surface, we can use the given information:

1. The water pressure at the surface of the ocean is 15 lb/in^2.
2. Below the surface, the water pressure increases by about 4.24 lb/in^2 for every 10 ft of descent.

Let's break down the problem and find the function step-by-step:

Step 1: Convert the depth from inches to feet.
Since the water pressure increases by about 4.24 lb/in^2 for every 10 ft, we need to convert the depth from inches to feet. Since 1 ft = 12 inches, we can divide the depth in inches by 12 to obtain the depth in feet.

depth_in_feet = depth_in_inches / 12

Step 2: Calculate the additional pressure due to depth.
The additional pressure due to depth can be calculated by multiplying the depth in feet by the pressure increase per 10 ft:

additional_pressure = (depth_in_feet / 10) * 4.24

Step 3: Calculate the total water pressure.
The total water pressure is the sum of the pressure at the surface and the additional pressure due to depth:

total_pressure = 15 + additional_pressure

Step 4: Convert the depth back to inches.
Since we expressed the additional pressure in terms of depth in feet, we need to convert it back to inches:

additional_pressure_in_inches = additional_pressure * (12 / 1)

Step 5: Add the additional pressure in terms of inches to the pressure at the surface.
Now we can rewrite the total water pressure expression using the additional pressure in terms of inches:

total_pressure = 15 + additional_pressure_in_inches

The final function f(x) that expresses the water pressure in pounds per square inch as a function of the depth in inches below the ocean surface is:

f(x) = 15 + (x / 10) * 4.24

Here, x represents the depth in inches below the ocean surface.

To write a function that expresses the water pressure as a function of depth below the ocean surface, we need to consider the relationship between depth and pressure. According to the given information, the water pressure increases by about 4.24 lb/in2 for every 10 ft of descent.

Let's break down the steps to create the function:

1. Convert the depth from inches to feet but still keeping it as a single value in feet.
- Since we know that 10 ft of descent causes an increase of 4.24 lb/in2 in pressure, we can infer that every 1 ft of descent corresponds to an increase of 0.424 lb/in2.
- Therefore, we divide the depth in inches by 12 to convert it to feet.

2. Calculate the pressure based on the converted depth.
- We know that at the surface of the ocean, the water pressure is 15 lb/in2.
- The increase in pressure for every 1 ft of descent is 0.424 lb/in2.
- So, the pressure at a given depth can be determined by adding the pressure at the surface to the increase in pressure due to the depth.

Based on these steps, the function f(x) can be written as:

f(x) = 15 + (x / 12) * 0.424,

where:
- x represents the depth in inches below the ocean surface, and
- f(x) represents the water pressure in pounds per square inch (lb/in2).