Choose the one alternative that best completes the statement or answers the question.
Solve for the indicated variable.
-$Q = Q _ { 0 } e ^ { - k t }$ for $k$
A) $k = \frac { \ln \left( Q - Q _ { 0 } \right) } { t }$
B) $k = - \frac { \ln \left( Q - Q _ { 0 } \right) } { t }$
C)$k = \frac { \ln \left( \frac { Q } { Q _ { 0 } } \right) } { t }$
D) $k = - \frac { \ln \left( \frac { Q } { Q _ { 0 } } \right) } { t }$

Question

Quizplus · Accepted Answer

To solve for $k$, we start with the given equation $Q = Q_0 e^{-kt}$. Dividing both sides by $Q_0$ gives $\frac{Q}{Q_0} = e^{-kt}$. Taking the natural logarithm of both sides yields $\ln\left(\frac{Q}{Q_0}\right) = -kt$. Finally, solving for $k$ gives $k = -\frac{\ln\left(\frac{Q}{Q_0}\right)}{t}$.

Choose the One Alternative That Best Completes the Statement or Answers