A scientist is studying bacteria

[rupeshj847]

A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?

(1) The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.

(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.




in the 2nd statement, it is given that the popltn will double with 1 hr remaining...that automatically the popltn will double in 3 hrs..so 1 hr from nw,it will be same...so this statement shud be sufficient also but it isnt

[RonPurewal]

the second statement gives no information about any other doubling.

you should KNOW that's an issue because it's mentioned in statement 1 ("The population just divided").
if you DON'T have that, then it's impossible to determine the interval between divisions.
(moreover, there could also be other divisions BETWEEN now and the 40,000.)

...so there are actually all kinds of unknowns here.

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if you have any further questions, please write out full words. (any future posts using things like "popltn" and "shud" will be deleted.)
thank you.

[ErinS514]

Hi Ron,

I've reviewed a few of the threads for this question, and I think it's safe to say that from statement 1, we know:
Population doubles every hour (and only every hour);
2 hours ago, population size was 1250;
Population size is now 5000.

But should we also assume that 2 hours ago was T -2 and is not part of the 4 hours? Another way to ask is: are we at T 0 with a population of 5000? Or could we possibly be at T +2 with destroy at T +4?

I read it as two hours ago could have been T 0 or T +1 but that it was within the 4 hours we were looking at, not that we have exactly 4 hours from now to evaluate. I guess it might just be a reading comprehension issue but I want to make sure I'm not skipping something that I should be aware of.

Thanks!

[RonPurewal]

the words "four hours FROM NOW" mean exactly what they say.

[shivrakesh65]

Hi Ron,

Please confirm my understanding to the above question.

The initial statement states that the Population of the Bacteria cells divide uniformly whenever the population doubles.

Since Statement says that the division just happened now , that means that the population just doubles & the last doubling happened 2 hours ago, so we can infer that the population doubles every 2 hours. Now after the recent doubling the population increased by 3750.
So if at T-2 the population is x, now at time T it is 2x & also we know that 2x=x+3750, which gives us the value of x, hence the population currently!

So basis this we can find out what is the population 4 hours from now, before the scientist destroys the bacteria.

Thanks.

[RonPurewal]

if you're talking about statement 1 (you just wrote "statement", and forgot to write the statement number)... you have the wrong specific numbers, but you have the right idea.

statement 1 says that the population has quadrupled SINCE the doubling that occurred 2 hours ago.
that's just what happened SINCE that doubling—so, in other words, the doubling that happened 2 hours ago is NOT INCLUDED in this observation.
(let's say you haven't seen a friend since last Monday. if i ask "have you seen her SINCE last Monday?", the answer is no.)

if the population has quadrupled then it's doubled TWICE SINCE that time—which means that the population doubles EVERY HOUR, not every 2 hours.

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on the other hand, since this is a DS problem, it's good enough to realize that this statement gives us the exact time interval between events that are n doublings apart—for SOME specific value of n.
as long as these are actually SPECIFIC numbers, this information is guaranteed to be sufficient—even if you have the actual numbers wrong, as you did here.