Solve for the indicated variable.
-$$P = 110 e ^ { 6 t } , \text { for } t$$
A) $\mathrm { t } = \frac { \ln \mathrm { P } + \ln 110 } { 6 }$
B) $t = \frac { \ln ( P - 110 ) } { 6 }$
C) $t = \frac { P } { 110 e ^ { 6 } }$
D) $t = \frac { \ln P - \ln 110 } { 6 }$

Question

Quizplus · Accepted Answer

To solve for $t$, we start with the given equation $P = 110e^{6t}$. We divide both sides by 110 to isolate $e^{6t}$ on one side: $\frac{P}{110} = e^{6t}$. Taking the natural logarithm (ln) of both sides to solve for $t$, we get $\ln\left(\frac{P}{110}\right) = 6t$, which simplifies to $t = \frac{\ln P - \ln 110}{6}$, matching choice D.

Solve for the Indicated Variable P=110e6t, for tP = 110 e ^ { 6 t } , \text { for } tP=110e6t, for t

Solve for the Indicated Variable $P = 110 e ^ { 6 t } , \text { for } t$