Question - Don't even know where to begin :0

[Skydiver]

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Here is a question I came across, don't even know where to begin with it.

A dilute disinfectant kills 90% of bacterial inoculum in 10 min. What is the shortest amout of time (in minutes) required to reduce the inoculum of 10^9 bacteria to less than 10 bacteria?

Any ideas?

 

[djnels01]

90 minutes

 

[djnels01]

90 minutes

I'm pretty sure this is the answer.

Since there is 10% of the colony left after each 10 minute interval, just multiply 10^9 by 0.1 and do this repeatedly until you get below 10. Should take you 9 seperate times to do so. 9 x 10 (min) = 90 minutes

 

[Skydiver]

That's what I thought too. without any calculations.
Problem is --- not an option
a)10
b)50
c)100
d)140
e)180

Please tell me how you arived at your answer

 

[djnels01]

That's what I thought too. without any calculations.
Problem is --- not an option
a)10
b)50
c)100
d)140
e)180

Please tell me how you arived at your answer

Then I would guess 10.

10^9 x 0.1 (same as 10%) = 10^8 x 0.1 = 10^7 x 0.1 = 10^6 ... etc. until you get to 10^0 which is 1.

Should be correct...

 

[yanon]

mathematically solving this problem
* = multiplication
y = number of 90% reductions
10^-1 = 1/10 which is the number of cells left after each reduction

10^9 * 10^(-1*y) = 10
10^9 * 10^-y = 10
10^(9-x) = 10
take the log of both sides
9-x = 1
x = 8

80 minutes should be the answer.

You can also solve this intuitively.

If 1000 = 10^3, 10% of 1000 is 100 = 10^2, 10% of 100 is 10 = 10^1
So after each reduction the total number of cells = 10 ^ (x-1)

So, you can just simply 10^9-1-1-1-1-1-1-1-1 = 10 ^1 = 10 cells

add up all the ones you subtracted, you should get 8 which is the total number of reductions.

 

[SOUNDMAN]

So the question asks for < 10 in the "shortest amount of time", so the answer is 100 essentially. 50 minutes wouldn't get you there, 80 is not an answer, and everything else is not the "shortest amount of time". so it must be 100 minutes

 

[djnels01]

dang it that's what I meant! I forgot a zero...

stupid me. I agree with soundman, I think 100 is correct