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

Answer:

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

Step-by-step 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:

$m = \frac{y_2-y_1}{x_2-x_1}$

Substitute the given point we have;

$m = \frac{3.3-1}{23-0} = \frac{2.3}{23} = 0.1$

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.