GED Mathematical Reasoning: Applications Of Functions

Example 1

The boiling point of water, represented by  (in degrees Celsius), is dependent upon the elevation  (in meters). This relationship can be modeled using the following function:

E = 1000(100 - t) + 580{(100 - t)}^2

At what elevation is the boiling point 105^{\circ}\mathrm{C}?

 

In this example, we are being given the temperature of 105 degrees and we need to determine the elevation that corresponds to that boiling point. In other words, we are being given the value for t and we need to use the function to find the corresponding value for E.

When we substitute 105 for t, we get:

E = 1000(-5) + 580{(-5)}^2
E = 1000(-5) + 580(25)
E = -5000 + 580(25)
E = -5000 + 14500
E = 9500 meters

So the elevation for which the boiling point of water is 105 degrees Celsius is:  9500 meters.

As a final note, we can write the equation in this example using function notation. The name of the function would be E and the variable in parenthesis would be t, since that is the variable used on the right side.

Function notation: E(t) = 1000(100 - t) + 580{(100 - t)}^2

Finding the elevation for a boiling point of 105 degrees would be a matter of calculating E of 105. We would substitute each t for the value 105 and simplify the right side as we just did to arrive at the result 9500 meters.

E(105) = 1000(100 - 105) + 580{(100 - 105)}^2
E(105) = 1000(-5) + 580{(-5)}^2
E(105) = 1000(-5) + 580(25)
E(105) = -5000 + 580(25)
E(105) = -5000 + 14500
E(105) = 9500 meters

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