For many, the Bitcoin market cap hitting $10 trillion is seen as only a matter of time as the price rises, but what happens to meme coins like Dogecoin during this time? In the past, these altcoins have outperformed Bitcoin in times of bullish rallies, and this is expected to continue with each bull cycle. Using past performances and the DOGE/BTC market cap ratio, Elon Musk’s GROK AI has projected how high the Dogecoin price would be if the Bitcoin market cap hits $10 trillion.Dogecoin Price To Eventually Cross $1The AI takes into account the current ratio of the Dogecoin market cap relative to that of Bitcoin, and also the highest point that this ratio has been in the past. Currently, the ratio sits at around 1.76%, but in times of bullish momentum, this ratio has previously risen higher. An example of this is back in the 2021 bull market.Back when the Dogecoin euphoria was at its peak, with billionaire Elon Musk personally promoting the meme coin, the ratio of the DOGE market cap to Bitcoin rose as high as 3.5%. Using this and translating it to a time when the Bitcoin market cap reaches $10 trillion with its price above $500,000, the AI has been able to project how high the Dogecoin price would be.In times of extreme bullishness, where the Dogecoin to Bitcoin ratio rises as high as 3-4%, it would mean that the DOGE market cap could rise as high as $170 billion. This takes into account the inflationary nature of the Dogecoin supply, which the AI takes into account. Using a conservative estimate of 151 billion DOGE coins in circulation at a time when the Bitcoin market cap hits $100 trillion.Since a rise to $10 trillion market cap is a 4.39x from here for the Bitcoin price, it is expected that the Dogecoin price would see a similar increase. Or in some cases, the meme coin could outperform as it has done in the past. Using this, the AI comes up with both a conservative and a bullish target for the Dogecoin price.In the conservative target, the Dogecoin price is sitting at $1.16 with a market cap of $176 billion, while the Bitcoin market cap hits $10 trillion. However, in the more bullish scenario, where the DOGE price outperforms as it did back in 2021, the AI sees the price rising as high as $2.32, which would be a $350 billion market cap at a circulating supply of 151 billion DOGE tokens. This would mean an 8-10x in contrast to Bitcoin’s 4.39x.Factors that could drive this outperformance are highlighted, including social media hype, which has previously driven up the price. The prospect of rising adoption through ETF approvals and DOGE payments also factors into this. However, the AI also highlights the fact that regulatory crackdowns, a decline in meme coin interest, and/or Bitcoin maintaining its high dominance on the market above 60% could all lead to the meme coin’s price staying below $1.