For a certain culture the equation $Q ( t ) = Q _ { 0 } e ^ { 0.9 t }$ , where Q 0 is an initial number of bacteria and t is time measured in hours, yields the number of bacteria as a function of time. How long will it take 600 bacteria to increase to 3,600? Please round the answer to the nearest tenth.
A) 2.0 hours
B) 1.0 hours
C) 7.0 hours
D) 5.0 hours
E) 4.0 hours

Question

Quizplus · Accepted Answer

To find the time $ t $, use the equation $ 3600 = 600 e^{0.9t} $. Solving for $ t $, we get $ e^{0.9t} = 6 $. Taking the natural logarithm of both sides, $ 0.9t = \ln(6) $. Thus, $ t = \frac{\ln(6)}{0.9} \approx 2.0 $ hours.

For a Certain Culture the Equation Q(t)=Q0e0.9tQ ( t ) = Q _ { 0 } e ^ { 0.9 t }Q(t)=Q0​e0.9t

For a Certain Culture the Equation $Q ( t ) = Q _ { 0 } e ^ { 0.9 t }$