college algabra ! urgent ! please help

[jb-]

Food poisoning is most often caused by E. coli bacteria. To test for the presence of E. coli in a pot of beef stew, a biologist performs a bacteria count on a small sample of the stew kept at 25°C. She determines that the count is 10 colony-forming units per milliliter (CFU/mL) and that the doubling time is 40 minutes under these conditions.

Find the hourly growth factor a

im really just lost on this. there are like 5 parts to this question and cant do any of them untill I am able to do this one. please help! the homework is due soon

 

[tkhunny]

r is an hourly growth rate.

\(\displaystyle r^{40/60} = 2\)

How were you thinking about it?

 

[HallsofIvy]

The crucial point is that "the doubling time is 40 minutes under these conditions".
If t is in minutes, then the number of "40 minutes intervals" is t/40. And the population will have doubled in that time: it will have doubled t/40 times so the, if the initial population is \(\displaystyle P_0\), then the population in t minutes is \(\displaystyle P(t)= P_0(2^{t/40})\). Now, take t= 1 hour= 60 minutes: \(\displaystyle P(60)= P_0(2^{60/40})= P_0(2^{3/2})\). The population has increased by \(\displaystyle 2^{3/2}\) times in one hour.