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The recommended percent p (in decimal form) of nitrogen (by volume) in the air that a diver breathes is given by p=105.07d+33, where d is the depth (in feet) of the diver. find the depth when the air contains 47% recommended nitrogen by (a) solving an equation, and (b) using the inverse of the function. round to the nearest tenth.

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The depth of the diver when the air contains 47% recommended nitrogen is -0.3 ft

To answer the question, we need to know what an equation is.

What is an equation?

An equation is a mathematical function that shows the relationship between two variables.

Given that he recommended percent p (in decimal form) of nitrogen (by volume) in the air that a diver breathes is given by p = 105.07d + 33, where d is the depth (in feet) of the diver.

Solving for the depth by solving the equation

To find the depth when the air contains 47% recommended nitrogen, we solve the equation with p = 47%

So, p = 105.07d + 33

47% = 105.07d + 33

0.47 = 105.07d + 33

0.47 - 33 = 105.07d

-32.53 = 105.07d

d = -32.53/105.07

d = -0.3096 ft

d ≅ -0.3 ft

Solving for the depth using the inverse function

Since p = 105.07d + 33

Making d subject of the formula, we have

d = (p - 33)/105.07

Substituting p = 47% = 0.47, we have

d = (0.47 - 33)/105.07

d = -32.53/105.07

d = -0.3096 ft

d ≅ -0.3 ft

So, the depth of the diver when the air contains 47% recommended nitrogen is -0.3 ft

Learn more about equations here:

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