ikokurin wrote:
It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one half of dish?
A) 10 days
B) 15 days
C) 24 days
D) 29 days
E) 29.5 days
It is a fairly simple problem, but I am struggling to express what happens here algebraically. Please help on algebra here.
Since it takes 30 days to fill the dish and the population
doubles each day, then the dish will be half full after 29 days: 1 day later (so after 30 days) the population will double again and the dish will be full.
Answer: D.
Algebraic approach:
Say initial population occupies 1/n of the disch.
Given: \(\frac{1}{n}*2^{30}=1\)
Question: if \(\frac{1}{n}*2^{x}=\frac{1}{2}\), then \(x=?\)
\(\frac{1}{n}*2^{x}=\frac{1}{2}\) --> \(\frac{1}{n}*2^{x}*2=1\) --> \(\frac{1}{n}*2^{x+1}=1\). Since we know that \(\frac{1}{n}*2^{30}=1\), then \(2^{x+1}=2^{30}\) --> \(x+1=30\) --> \(x=29\).
Hope it helps.