Writing linear functions

Question

The pressure p of water on a diver's nody is a linear function of the diver's depth, x. At the water's surface the pressure is 1 atmosphere. At a depth of  100 ft, the pressure is about 3.92 atmospheres. Find the linear function that relates p to x.

Answer 1

Hi Mirsha,

 

The question says that p is a linear function of x.

 

The general formula of a linear function is-->  p(x) = mx + b

 

Now let's substitute the pressure of 1 at zero depth--> 1 = 0m + b

 

b = 1

 

Now let's substitute the pressure of 3.92 at a depth of 100 feet--> 3.92 = 100m + 1

 

Subtract 1 from both sides-->2.92 = 100m

 

Divide both sides by 100--> m = .0292

 

So the linear function is--> p(x) = .0292x + 1

 

Dan