Solve for the indicated variable.
-$I = \frac { \mathrm { w } } { \mathrm { P } } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)$, for $\mathrm { s }$
A) $s = - \frac { 3 \ln \left( 1 - I P _ { W } \right) } { a }$
B) $s = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IP } } { \mathrm { w } } \right)$
C) $\mathrm { s } = \frac { \mathrm { IwP } \cdot \ln ( 1 - \mathrm { a } ) } { 3 }$
D) $\mathrm { s } = \frac { 3 \cdot \ln ( 1 - \mathrm { a } ) } { \mathrm { IwP } }$

Question

Quizplus · Accepted Answer

To solve for $s$, we first isolate the exponential term: $I = \frac { w } { P } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)$ implies $1 - \frac{IP}{w} = e^{-as/3}$. Taking the natural logarithm of both sides gives $\ln\left(1 - \frac{IP}{w}\right) = -\frac{as}{3}$, which rearranges to $s = -\frac{3}{a} \ln\left(1 - \frac{IP}{w}\right)$.

Solve for the Indicated Variable I=wP(1−e−as/3)I = \frac { \mathrm { w } } { \mathrm { P } } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)I=Pw​(1−e−as/3)

Solve for the Indicated Variable $I = \frac { \mathrm { w } } { \mathrm { P } } \left( 1 - \mathrm { e } ^ { - \mathrm { as } / 3 } \right)$