00:01
So we'll start off with the question that has us wondering that a leprechaun places a magic penny under a girl's pillow.
00:09
So at the first day, the penny is a single penny, but then it turns into two pennies the next day.
00:16
And then it turns into four pennies the next day and further on eight, then 16 and then 32.
00:23
So this is the day that the leprechaun puts it.
00:27
So this is day zero.
00:28
And then after day one it's two on day two it's four on on day three it's eight on day four it's six and day five it's 32 so we notice something that two raised to the power of zero is equals to one two raise to the power of one is equals to two two raised to the power of two is equals to four so we see that the days it follows through is two raise to the power of the number of the of days gives us the pennies that will exist.
01:04
For example, if we go for day number 20, we will have the penny as 2 to the power of 20.
01:14
That is 1048576 pennies.
01:19
Now, if we assume that one penny is, so since we have that with us, now we have, we go forward with how many days it would take for her to have one billion dollars so in one dollar we have a hundred pennies so in one billion dollars we will have a hundred billion pennies and now we know that since a billion has nine zeros in it hundred billion would have eleven of those so we go with that we write these down these are eight zeros and this is 11 zeros and we need to find out with 2 to the power of t where t is the number of days.
02:12
So following suit with that, we will key in through trial to trial.
02:18
So we key in our first value, which let's take as two raise to the power of 30.
02:26
Since we got 20 near to about seven zeros will key in 30 and see how many zeros it brings to us.
02:36
So the value is 1 .0 .73774714...