Find the associated exponential decay model. $Q = 7,000$ when $t = 0$ ; Half-life = 9

A) $Q = 7,000 - e ^ { - \frac { t } { 9 } }$
B) $Q = 7,000 e ^ { - \frac { t ( \ln 2 ) } { 9 } }$
C) $Q = 7,000 + e ^ { \frac { t ( \ln 2 ) } { 9 } }$
D) $Q = 7,000 e ^ { - \frac { t } { 9 } }$
E) $Q = 7,000 e ^ { \frac { t } { 9 } }$

Question

Find the associated exponential decay model.   $Q = 7,000$ when $t = 0$ ; Half-life = 9
 
A) $Q = 7,000 - e ^ { - \frac { t } { 9 } }$
B) $Q = 7,000 e ^ { - \frac { t ( \ln 2 ) } { 9 } }$
C) $Q = 7,000 + e ^ { \frac { t ( \ln 2 ) } { 9 } }$
D) $Q = 7,000 e ^ { - \frac { t } { 9 } }$
E) $Q = 7,000 e ^ { \frac { t } { 9 } }$

Quizplus · Accepted Answer

The correct model for exponential decay, given a half-life, is $Q = Q_0 e^{-\frac{t(\ln 2)}{\text{half-life}}}$, where $Q_0$ is the initial quantity. Here, $Q_0 = 7,000$ and the half-life is 9, so the model is $Q = 7,000 e^{-\frac{t(\ln 2)}{9}}$.

Find the Associated Exponential Decay Model Q=7,000Q = 7,000Q=7,000 When t=0t = 0t=0

Find the Associated Exponential Decay Model $Q = 7,000$ When $t = 0$