Answer to Question #280568 in Differential Equations for Muffin

Question

In 8: 00 AM, the population of a bacteria is 1000. At 11: 30 AM, the number of bacteria triples. At what time will the population become 300 times the initial population of bacteria?

Answer 1

Initial population of bacteria (at 8:00 AM) =1000

300 times the initial population of bacteria = 1000*300 = 300,000

Number of bacteria tripled at 11:30 AM = 3.5 hours

The exponential form is;

$P(t)=P_0e^{rt}$

$300000=1000*3^{(\frac{t}{210})}$

$ln(300)={(\frac{t}{210})}\ln3$

${(\frac{t}{210})}={(\frac{ln300}{ln3})}$

$t={(\frac{ln300}{ln3})}\times210$

$t=1090.28\approx1090 mins$

t = 18 hours 10 mins

$Time=8:00 AM+18hours10mins=2:10AM$