Question

The pressure at sea level is 11 atmosphere and increases at a constant rate as depth increases. When Sydney dives to a depth of 23 meters, the pressure around her is 3.3 atmospheres. The pressure p in atmospheres is a function of x, the depth in meters.

Answer 1

The function
`p(x) = 0.1x+1` , where x is the depth in meters.

Explanation:

As per the statement: The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases.

Then, we have the two points i,e (0, 1) and (23, 3.3).

An equation of the line is in the form of y=mx+b where m is the slope or rate of the line and b is the y-intercept.

Let x represents the depth in meters and p(x)= y represents the pressure in atmosphere.

Calculate slope of the line:

Slope of line(m) is given by:

`m = (y_2-y_1)/(x_2-x_1)`

Substitute the given point we have;

`m = (3.3-1)/(23-0) = (2.3)/(23) = 0.1`

Then, our equation of line become:

y = 0.1x + b .....[1]

To solve for b;

Substitute the point (0, 1) in [1];

`1 = 0.1(0)+b`

`1 = b`

Our equation for this line become: y = 0.1x +1

Now, we write this for x as a function of p,

i.e, p(x) = 0.1x + 1

Then, the function formula become;

`p(x) = 0.1x+1` where x is the depth in meters.