Am I doing this right (Check my math)?

RESmonkey

Diamond Member
May 6, 2007
4,818
2
0
Bacteria Growth - A colony of bacteria is grown underideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 h there are 10,000 bacteria. At the end of 5 h there are 40,000 bacteria. How many bacteria were present initially?

What I did:

I used a generic function like this: y = (y initial)e^(-kt)

I made did:
40,000 = 10,000e^(2k)

Solved for k, k = 1n(4) / 2

Plugged k into this:

10,000 = Xe^(3k)
X = 1250

1250 bacteria were there initially?

Thanks


 
Apr 17, 2005
13,465
3
81
they double every hour, so i guess at the end of 1 hr there were 2500. does that make sense? i already butchered someone elses problem so dont go by what i say. :p
 

nycxandy

Diamond Member
Apr 11, 2001
3,731
0
76
Originally posted by: Inspector Jihad
they double every hour, so i guess at the end of 1 hr there were 2500. does that make sense? i already butchered someone elses problem so dont go by what i say. :p

That would apply if it increased linearly, but that's not the case here.
 

rocadelpunk

Diamond Member
Jul 23, 2001
5,589
1
81
Yep everything is fine.

You have two equations and they gave you two pts on what would be the graph.

40,000=P*e^5k
10,000 = P*e^3k


just divide these two and you're left with 4 = e^2k, use natural log property and you get your k = ln(4) / 2

Then as you did, plug back into either one.

:beer: