Solve for the indicated variable.
-$$P = 30,000 \cdot e ^ { t / 3 } \text {, for } t$$
A) $t = 3 \cdot \ln \frac { P } { 3000 }$
B) $t = 30 \cdot \ln \mathrm { P }$
C) $t = \ln ( 30 \mathrm { P } )$
D) $t = 3 \cdot \ln \frac { P } { 30,000 }$

Question

Quizplus · Accepted Answer

To solve for $t$, we start with the given equation $P = 30,000 \cdot e^{t/3}$. We divide both sides by 30,000 to isolate $e^{t/3}$ on one side: $\frac{P}{30,000} = e^{t/3}$. Taking the natural logarithm (ln) of both sides to solve for $t/3$, we get $ln\left(\frac{P}{30,000}\right) = \frac{t}{3}$. Multiplying both sides by 3 to solve for $t$, we obtain $t = 3 \cdot ln\left(\frac{P}{30,000}\right)$.

Solve for the Indicated Variable P=30,000⋅et/3, for tP = 30,000 \cdot e ^ { t / 3 } \text {, for } tP=30,000⋅et/3, for t

Solve for the Indicated Variable $P = 30,000 \cdot e ^ { t / 3 } \text {, for } t$