Update hip-782.md (#783)

Signed-off-by: Leemon Baird <lbaird@users.noreply.github.com>
Signed-off-by: Michael Garber <michael.garber@swirldslabs.com>
Co-authored-by: Michael Garber <michael.garber@swirldslabs.com>

HIP/hip-782.md

@@ -11,7 +11,7 @@ release: v0.40.0
 created: 2023-08-01
 discussions-to: https://github.com/hashgraph/hedera-improvement-proposal/pull/782
 replaces: 406
-updated: 2023-08-09
+updated: 2023-08-10
 ---
 
 Note: This hip does not replace all of hip-406 Staking. It replaces only replaces a small part. Otherwise, hip-406 still stands.
@@ -28,18 +28,17 @@ This HIP describes a change to the staking reward system for proof of stake desc
 
 ## Specification
 
-In the original HIP, there is a setting `stakingRewardRate`, and rewards are given at that rate until the unreserved balance of account `0.0.800` is empty, at which point it abruptly drops to simply distributing each day whatever came in to that account the previous day, such as through transaction fees.  And there was originally a setting for the max reward emission per day. 
+In the original HIP, there is a setting `stakingRewardRate`, and rewards are given at that rate until the unreserved balance of account `0.0.800` is empty, at which point it abruptly drops to simply distributing each day whatever came in to that account the previous day, such as through transaction fees.   
 
-The change is to remove both of those settings, and have `stakingRewardRate` automatically change each day, based on the balance of `0.0.800` and three settings: `maxRewardRate`, `rewardBalanceThreshold`, and `maxStakeRewarded`.  The `maxRewardRate` (in tinybars earned per hbar staked per day) is the rate to pay normally (i.e., when `0.0.800` has a large balance, and not too many hbars are staked for reward). When the balance of `0.0.800` drops below `rewardBalanceThreshold` (in tinybars), then the `stakingRewardRate` drops smoothly as the balance drops. If the hbars staked for reward exceed `maxStakeRewarded` (in tinybars), then there is a further decrease (which replaces the original absolute limit on hbars emitted per day).
+The change is to remove this settings, and have `stakingRewardRate` automatically change each day, based on the balance of `0.0.800` and three settings: `maxRewardRate`, `rewardBalanceThreshold`, and `maxStakeRewarded`.  The `maxRewardRate` (in tinybars earned per hbar staked per day) is the rate to pay normally (i.e., when `0.0.800` has a large balance, and not too many hbars are staked for reward). When the balance of `0.0.800` drops below `rewardBalanceThreshold` (in tinybars), then the `stakingRewardRate` drops smoothly as the balance drops. If the hbars staked for reward exceed `maxStakeRewarded` (in tinybars), then there is a further decrease (which replaces the original absolute limit on hbars emitted per day).
 
-
 Let `unreservedBalance` (in tinybars) be the balance of account `0.0.800` minus the amount of rewards that have been earned but not yet distributed. Let `stakedForReward` (in tinybars) be the total number of hbars on Hedera that have been staked for reward (so it ignores accounts that stake but decline a reward). Then each day, just before the HIP-406 reward calculations are performed using `stakingRewardRate`, recalculate `stakingRewardRate` as follows (implemented with equivalent results, but using integer calculations, rather than the real-number calculations shown):
 
 ```
 //A real number proportional to the unreserved balance, from 0 for empty, up to 1 at the threshold.
 balanceRatio = min(unreservedBalance, rewardBalanceThreshold) / rewardBalanceThreshold;
 
-stakingRewardRate = maxRewardRate 
+stakingRewardRate = maxRewardRate * stakedForReward
                       * balanceRatio * (2 – balanceRatio) 
                       * min(1, maxStakeRewarded / stakedForReward)