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Am I doing this right (Check my math)?

R

RESmonkey

Diamond Member
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


 
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. 😛
 
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. 😛
Click to expand...

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