Solve for the indicated variable.
-$I = \frac { n } { R } \left( 1 - e ^ { - a w / 3 } \right)$, for $w$
A) $w = \frac { 3 \cdot \ln ( 1 - a ) } { \operatorname { In } R }$
B) $w = - \frac { 3 \ln ( 1 - \operatorname { IRn } ) } { a }$
C) $w = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IR } } { \mathrm { n } } \right)$
D) $w = \frac { \operatorname { In } R \cdot \ln ( 1 - a ) } { 3 }$

Question

Quizplus · Accepted Answer

To solve for $w$, we start with the given equation $I = \frac { n } { R } \left( 1 - e ^ { - a w / 3 } \right)$. We isolate the exponential term and then solve for $w$. Rearranging the equation and solving for $w$ leads to $w = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IR } } { \mathrm { n } } \right)$, which matches choice C.

Solve for the Indicated Variable I=nR(1−e−aw/3)I = \frac { n } { R } \left( 1 - e ^ { - a w / 3 } \right)I=Rn​(1−e−aw/3)

Solve for the Indicated Variable $I = \frac { n } { R } \left( 1 - e ^ { - a w / 3 } \right)$