Suppose that in order to remove x% of the pollution from the oil spill, it costs C(x) =...

Question:

Suppose that in order to remove {eq}x% {/eq} of the pollution from the oil spill, it costs {eq}C(x) = \frac{15x}{100-x} {/eq} thousands of dollars.

a. How much does it cost to remove 25% of the pollution?

b. How much does it cost to remove 50% of the pollution?

Rational Functions

When we have a variable in the denominator of a function, then we need to be careful in that we cannot have a denominator equal to zero. Thus, the domain of such a function is restricted in a way that x cannot cause this to happen.

Answer and Explanation:

a. Since x represents the amount of pollution that we wish to remove, we can evaluate our function at 25 to calculate the costs of removing 25% of the pollution.

{eq}\begin{align*} C(25) &= \frac{15(25)}{100-25} \\ &= \frac{375}{75}\\ &= 5 \end{align*} {/eq}

Therefore, it would cost $5,000 to remove 25% of the pollution from this oil spill.


b. Let's repeat this calculation to see how much it would cost to remove 50% of the pollution instead. We can evaluate our function at 50 to achieve this.

{eq}\begin{align*} C(50) &= \frac{15(50)}{100-50} \\ &= \frac{750}{50}\\ &= 15 \end{align*} {/eq}

This time, our calculation resulted in value of 15, meaning that it would cost $15,000 to remove 50% of the pollution from this oil spill.


Learn more about this topic:

Loading...
Rational Function: Definition, Equation & Examples

from GMAT Prep: Help and Review

Chapter 10 / Lesson 11
165K

Related to this Question

Explore our homework questions and answers library