1950 AHSME Problems/Problem 11

Problem

If in the formula $C =\frac{en}{R+nr}$ , $n$ is increased while $e$ , $R$ and $r$ are kept constant, then $C$ :

$\textbf{(A)}\ \text{Increases}\qquad\textbf{(B)}\ \text{Decreases}\qquad\textbf{(C)}\ \text{Remains constant}\qquad\textbf{(D)}\ \text{Increases and then decreases}\qquad\\ \textbf{(E)}\ \text{Decreases and then increases}$

Solution

Assume that the constants are positive, as well as $n.$

WLOG let $e,$ $R,$ and $r$ all equal $1.$ Then $C=\frac{n}{1+n}.$ We can see that as $n$ increases from $0,$ it slowly approaches $1.$ Therefore, $C$ $\boxed{\mathrm{(A)}\text{ }\mathrm{ Increases}.}$

If $r$ and $R$ were positive and $e$ was negative, then $C$ would decrease, for example.

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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1950 AHSME Problems/Problem 11

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