The predicted cost C (in thousands of dollars) for a company to remove p% of a chemical from its waste water is given by the model $C = \frac { 124 p } { 90,000 - p ^ { 2 } } , 0 \leq p

Question

The predicted cost C (in thousands of dollars) for a company to remove p% of a chemical from its waste water is given by the model  $C = \frac { 124 p } { 90,000 - p ^ { 2 } } , 0 \leq p < 100$ .  
Write the partial fraction decomposition for the rational function.Verify your result by using the table feature of a graphing utility to create a table comparing the original function with the partial fractions.
 
A) $\frac { 1 } { 300 - p } - \frac { 1 } { 300 + p }$
B) $\frac { 124 } { 300 - p } - \frac { 124 } { 300 + p }$
C) $\frac { 62 } { 300 - p } - \frac { 62 } { ( 300 - p ) ^ { 2 } }$
D) $\frac { 62 } { 300 - p } - \frac { 62 } { 300 + p }$
E) $\frac { 62 } { 300 - p } + \frac { 62 } { 300 + p }$

Quizplus · Accepted Answer

The denominator $90,000 - p^2$ can be factored as $(300 - p)(300 + p)$. To find the partial fraction decomposition, we need to express the given function in the form of $\frac{A}{300 - p} + \frac{B}{300 + p}$. Multiplying both sides by the common denominator, we get $124p = A(300 + p) + B(300 - p)$. Solving for A and B, we find that $A = -B = 62$, leading to the decomposition $\frac{62}{300 - p} - \frac{62}{300 + p}$.

The Predicted Cost C (In Thousands of Dollars) for a Company