Question

The depth and the corresponding pressure form an arithmetic sequence, where the depth

represents the number of the term and the corresponding distance represents the value of
the term. What is the pressure, in pounds per square inch, that a scuba diver will
experience when they are 130 feet underwater?

Answer 1

40 psi

Explanation:

We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth

The data is given from depth of 40 feet

At 40 feet, pressure = 10 psi

At 55 feet, pressure = 15 psi

At 70 feet pressure = 20 psi

We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure per 15' is
`= (d-40)/(15)\cdot 5`

But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi

So the equation that connects depth (d) and pressure (p) is:

`p = (d - 40)/(15)\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = (130-40)/(15)\cdot 5 + 10\\= (90)/(15)\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\`

If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3

Hope that helps