Vesting Shares and the Vesting Fund
I am doing some research to support a proposal post for 
Old-timey Hivers/Steemians will probably be more familiar, but it's not a topic that comes up often, so it's entirely possible most of those active now are not aware at all, but "Hive Power" does not actually exist. You do not have a balance of "powered up Hive" in the system, rather you have shares in the vesting fund. The vesting fund is a big pool of Hive that all those with vesting shares own collectively. Every new block, new Hive is added to the vesting fund as part of inflation, and also every time someone powers up or receives rewards (author, curator, witness) simultaneously new Hive is added to the fund and new Vesting Shares are created. The inverse happens whenever someone powers down.
As a consequence of the inflation being added to the vesting fund and a different amount of Vesting Shares existing at any one time, the rate of Hive per MVests changes over time. In principle this should not be completely predictable, because it also depends on demand for Hive Power, which can change over time. Yet in practice this element has only rarely had an impact. There is a notable change after the Hive/Steem split, but no clear change at any other point after Hard Fork 16 which drastically altered the Steem inflation schedule all the way back in December 2016.
Historic Hive per MVests
Using the Wayback Machine I reviewed snapshots of steemd.com throughout Steem and Hive's existance, and charted the value of Steem per MVest over time. Sadly hiveblocks.com snapshots do not contain enough data to continue the chart post-fork, so I just used data from the latest block (as of time of writing) on hiveblockexplorer.com. It differs only slightly from Steem, so I think that there was only a small difference overall between the two post-fork.
After hard fork 16 (December 2016), Steem per MVest is basically a straight line until the Hive/Steem split. Then, both raise their slope slightly, but are again just a straight line from there.
Deriving a Formula
From this data, I can derive a formula that predicts Hive per MVest at any time after March 6th, 2020 (this is the last snapshot of steemd.com available before the split). You can use this formula if you want to calculate historic Curation Rewards and Author Rewards accurately in Hive or in Dollars rather than in Vests. It's not perfect but it's more than good enough for accuracy.
Hive per MVests = 510.252 + (Current time - "06/03/2020 01:06:48") * 0.04485917121
The time bracket is in days, so basically we are just adding 0.04485917121 Hive per MVest for every day past the last known snapshot.