Is there a faster way?

[email protected] wrote:The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1000 to 500000?

18

Does anyone know a faster way?

I dont know it is fast or not but I solved this without paper.

you can interpret this ques as
500000 = 1000( 1 + 2*1 + 2*2*1 + 2*2*2*1 +.. )
500 = (1 + 2 + 4 + 8 + .. till nth minute ) (sum of GP series)
500 = (2^n - 1)/(2-1)
500 = 2^n -1 or 501 = 2^n
now value of n for which 2^n closest to 501 shall be 9 because 2^9=512
Therefore total time shall be 9 times 2 minutes which is equal to 18 mins.

I hope it helps.

Whenever we see a problem which has doubling(tripling, multiplying) every x time units, then it implies that the problem is a geometric series problem.
If sum of the geometric series is asked, then use the following formula:

S = a (1 -r^n)/(1 - r)
where
a: starting value
r: common ratio
n: the nth term.

Thanks Sachindh for the nice explanation of the solution.

it can be cal verbally , no need to cal and it took me 30 sec approx

current 1000
2000
4000
8000
16000
32000
64000
128000
256000
512000 ----- 9 instance...earc instance 2 mins ...So 9*2 =18mins

yes!

formula

1000( 2^x) = 500000

2^x = 500

x ~ 9

hence 18 minutes

yes!

I had also solved it using ronnie's method

I feel proud