i don't know why coinmarketcap has become popular for people as a go to when they want to check the price! it is the worst place you can check the price from. it gives you the average, the charts aren't accurate,...
but the actual lowest price of bitcoin recoded ~
there you go:
https://bitcoincharts.com/charts/mtgoxUSD#czsg2010-06-01zeg2010-08-17ztgSzm1g10zm2g25$0.05 on July 2010.
since you love (the meaningless) market cap so much by July 2010 supply of bitcoin was
19 months * ~30 days * 144 blocks/day * 50
BTC/block = 4,104,000
market cap of bitcoin = 4,104,000 * 0.05 = ~$205,200
the bitcoin sites on the internet are different. they have their own graphics. but the local wallet site, always accurate to see the price of bitcoin and its exchange rate to local currency.