Population drop word problem -- help with the Algebra please

[FactChecker]

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

No. If a tenth are killed, that is 100,000 killed and 1,000,000-100,000 = 900,000 remaining.

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

A tenth of 900,000 are killed. That is 90,000 killed and 900,000 - 90,000 = 810,000 remaining.
At 30 minutes: a tenth of 810,000 are killed. That is 81,000 killed and 810,000 - 81,000 = 729,000 remaining.
...
So the approach of calculating the killed at each step requires that you keep subtracting the killed from the remaining living at each time step.
It's easier to directly calculate the living by multiplying the remaining living at each step by 0.9. Then you don't have to keep doing a subtraction:
10^6 * 0.9 = 900,000
900,000 * 0.9 = 810,000
810,000 * 0.9 = 729,000
...
After $n*10$ minutes, there are $10^6*0.9^n$ remaining.

 

[symbolipoint]

No. If a tenth are killed, that is 100,000 killed and 1,000,000-100,000 = 900,000 remaining.A tenth of 900,000 are killed. That is 90,000 killed and 900,000 - 90,000 = 810,000 remaining.
At 30 minutes: a tenth of 810,000 are killed. That is 81,000 killed and 810,000 - 81,000 = 729,000 remaining.
...
So the approach of calculating the killed at each step requires that you keep subtracting the killed from the remaining living at each time step.
It's easier to directly calculate the living by multiplying the remaining living at each step by 0.9. Then you don't have to keep doing a subtraction:
10^6 * 0.9 = 900,000
900,000 * 0.9 = 810,000
810,000 * 0.9 = 729,000
...
After $n*10$ minutes, there are $10^6*0.9^n$ remaining.

From his comment of post #28 and #30, opus may finally understand.

 

[opus]

No. If a tenth are killed, that is 100,000 killed and 1,000,000-100,000 = 900,000 remaining.A tenth of 900,000 are killed. That is 90,000 killed and 900,000 - 90,000 = 810,000 remaining.
At 30 minutes: a tenth of 810,000 are killed. That is 81,000 killed and 810,000 - 81,000 = 729,000 remaining.
...
So the approach of calculating the killed at each step requires that you keep subtracting the killed from the remaining living at each time step.
It's easier to directly calculate the living by multiplying the remaining living at each step by 0.9. Then you don't have to keep doing a subtraction:
10^6 * 0.9 = 900,000
900,000 * 0.9 = 810,000
810,000 * 0.9 = 729,000
...
After $n*10$ minutes, there are $10^6*0.9^n$ remaining.

I really need to work on my reading comprehension! Thanks for pointing that out to me.

 

[symbolipoint]

I really need to work on my reading comprehension! Thanks for pointing that out to me.

Most of Reading Comprehension for Mathematics is very, very literal.