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 2323 meters, the pressure around her is 3.33.3 atmospheres. The pressure pp in atmospheres is a function of xx, the depth in meters. Write the function's formula.

Answer 1

Answer:

p(x) = 0.1x + 1

Step-by-step explanation:

Pressure at sea level = 1 atmosphere

Depth dove by Sydney = 23 meters

Pressure at a depth of 23 meters = 3.3 atmospheres

So,

Pressure at a depth of 23 meters = Pressure at sea level + k * Depth dove by Sydney

where k is  the diving rate constant

=> 3.3 = 1 + k(23)

=> 3.3 = 23k + 1

Subtracting 1 from both the sides, we get

3.3 - 1 = 23k + 1 -1

Cancelling out the +1 and -1 from the right side, we get

2.3 = 23k

=> 23k = 2.3

Dividing both sides by 23, we get

$\frac{23k}{23} = \frac{2.3}{23}$

Cancelling out the 23's from the top and bottom of the left side, we have

k = 0.1

Plugging in the value of k in the equation, we get

Pressure at a particular depth = Pressure at sea level + k * Depth dove by Sydney

p(x) = 1 + k(x)     [where p(x) is the pressure at a depth x]

=> p(x) = 1 + 0.1(x)

=> p(x) = 0.1x + 1