- #26

opus

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At 10 minutes: a tenth of 10^6 bacteria are killed. This leaves 100,000 remaining.

At 20 minutes : a tenth of the 100,000 bacteria are killed. This leaves 10,000 remaining.

At 30 minutes: a tenth of the 10,000 are killed. This leaves 1000 remaining.

This is the process that is happening.

Now I am asked

*at which period will 70% of the bacteria be killed, or 30% of the bacteria remain?*

The initial population of the bacteria is 10^6. I want to find 30% of 10^6. Mathematically, I want 0.3(10^6). This is one side of the equation, where I list what I am asked for.

For the other side, I express the process of decay that is happening, which I listed in words previously.

I know that I am given an initial population of 10^6, and every ten minutes, the current population drops by a tenth, or (1/10).

To express this process mathematically, I have the given population dropping by a tenth every ten minutes, or 10^6(1/10)(1/10)(1/10)..... or 10^6(1/10)^x.

So combining both of these, I have ##0.3\left(10^6\right)=10^6\left(\frac{1}{10}\right)^x##

This is my train of thought here, looking at it as

*bacteria killed*. The LHS represents 30% of the initial bacteria population, which means 70% was killed. The RHS represents the decay process. Could you be so kind as to highlight in bold where I make a faulty statement?