These questions are pertaining to Linear Equations

Question

The pressure P of water on a diver's body is a linear function of a 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.

 

a) Find a linear function that relates P to x.

b) Compute the pressure, to the nearest hundredth, at a depth of 10 fathoms (60 ft)

Answer 1

a. You can find the function by using the two points given, (0 , 1) and (100 , 3.92).  Find the slope.

 

m = (y₂ - y₁) / (x₂ - x₁) = (3.92 - 1) / (100 - 0) = 2.92/100 = 0.0292

 

You are given the y-intercept, (0 , 1), so now you can write the equation.

 

P = 0.0292x + 1

 

b. Plug in 60 for x to solve for the pressure.

 

P = 0.0292(60) + 1

P = 2.752

 

At a depth of 10 fathoms (60 feet), the pressure is 2.752 atmospheres.

Answer 2

(a)

 

P(x) = ax + b

 

At x = 0:

 

P = 1 ⇒ 1 = a(0) + b ⇒ b = 1

 

P(x) = ax + 1

 

At x = 100:

 

P = 3.92 ⇒ 3.92 = a(100) + 1 ⇒ a = (3.92 - 1)/100 = 0.0292

 

P(x) = 0.0292x + 1, P in atm, x in ft

 

(b)

 

P(60) = 0.0292(60) + 1 = 2.752 atm ≅ 2.75 atm