Question

The pressure at sea level is 111 atmosphere and increases at a constant rate as depth increases. When Sydney dives to a depth of 232323 meters, the pressure around her is 3.33.33, point, 3 atmospheres.

Answer 1

Question: The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases. When Sydney dives to a depth of 23meters, the pressure around her is 3.33, point, 3 atmospheres.

The pressure p in atmospheres is a function of x, the depth in meters.

Write the function's formula.

Anwser: 0.1x + 1

Answer 2

`P(x)=0.1x+1`

Explanation:

Please consider the complete question.

The pressure at sea level is 1 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. Write the function's formula.

We have been given two points as (0,1) and (23,3.3). Our required function's formula would be the line which passes through these points.

First of all we will find slope of line passing through points (0,1) and (23,3.3).

`m=(3.3-1)/(23-0)=(2.3)/(23)=(23)/(230)=0.1`

Now we will find equation of this line in point-slope form
`y-y_1=m(x-x_1)`.

Upon substituting
`m=0.1\text{ and }(x_1,y_1)=(0,1)`, we will get:

`y-1=0.1(x-0)`

`y-1=0.1x`

`y-1+1=0.1x+1`

`y=0.1x+1`

Our equation for this line will be
`y=0.1x+1`.

Now let us write this for x as a function of p,

`P(x)=0.1x+1`

Therefore, our required function formula would be
`P(x)=0.1x+1`.