求解一道模考数学题，没看懂，谢谢

xylstc · 发表于 2017-2-19 22:10:32

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.

我叫Fred · 发表于 2017-2-20 00:28:24

Let the current time be 10:00AM. What will be the cell population at 2:00PM?

1.
Let the cell population be x just before @ 10-2 = 8AM
After doubling; population = 2x
After that it has quadrupled; 2x*4 = 8x
10:00AM, the population is 8x

And;
8x-2x=3750
6x = 3750
x = 625
We know the count was 625*2 = 1250 @8AM
We know the count is 625*8 = 5000 @10AM
We also know that the bacteria divided 2 times within last 2 hours;
But, we don't know that constant interval yet after which bacteria divide.

The cell could have divided at 8:50AM and 9:40AM with 50 minutes interval
The cell could have divided at 8:41AM and 9:22AM with 41 minutes interval
The cell could have divided at 8:59AM and 9:58AM with 59 minutes interval

We wouldn't know exactly what will be the cell count after 4 hours unless we know that constant interval.
Not Sufficient.

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

@1:00PM, the cell count = 40,000
Still, we don't know the interval. What if bacteria divides every minute or divides every hour.
Not sufficient.

Combing both;
We know
@10:00AM: count=1250
@1:00PM: count=40,000

Thus it must have divided 5 times in 5 hours
8:00AM: 1250
9:00AM: 2500
10:00AM:5000
11:00AM: 10000
12:00PM: 20000
1:00PM: 40000

@2:00PM
count=80000
Sufficient.

Ans: "C"

xylstc · 发表于 2017-2-20 22:24:08

Thank you

求解一道模考数学题，没看懂，谢谢

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