Question

A strain of bacteria doubles in numbers each day, if today there are $16$ million bacteria, how many days ago were there $500,000$ bacteria?

Answer 1

If the number of bacteria is $x$ today,

then no. of bacteria after 1 days $=2x$

no. of bacteria after 2 days $=2x\left(2\right)=4x$

after 3 days $=8x=2^{3}x$

after $n$ days $=2^{n}x$

Let $n$ days ago, there were $500,000$ bacteria

then

$500,000\times 2^n=16,000,000$

$2^n=32$

$2^n=2^5$

$\Rightarrow n=5$