A bacterial culture grows exponentially; that is, P(t) = 100 $\mathrm { e^{kt} }$ , where P(t) is the size of the culture at time t hours. Suppose that after 2 hours the size of the culture is 400. What is k (approximately)?
A) 3
B) 0.69
C) 0.06
D) 0.48
E) none of these

Question

Quizplus · Accepted Answer

To find $k$, use the given information $P(2) = 400$ and the formula $P(t) = 100e^{kt}$. Substituting the values gives $400 = 100e^{2k}$. Dividing both sides by 100 gives $4 = e^{2k}$. Taking the natural logarithm of both sides gives $ln(4) = 2k$, so $k = \frac{ln(4)}{2} \approx 0.69$.

A Bacterial Culture Grows Exponentially; That Is, P(t) = 100 ekt\mathrm { e^{kt} }ekt

A Bacterial Culture Grows Exponentially; That Is, P(t) = 100 $\mathrm { e^{kt} }$