How to graph acceleration from an equation given a sample period?

I am unfamiliar with Mathematica and the necessary syntax to approach visualize acceleration over time. I would appreciate some assistance or reference to a starting point on how to go about solving this problem. Please note that I have never used Mathematica before.

I am writing some game code that handles a third-person camera rotation that increases in speed over time (acceleration) as the left or right directional buttons are held down.

I am currently polling the directional button once every t milliseconds where sampling begins at the base and increases linearly every 100ms by a delta towards a maximum sampling rate.

So, for example (in microseconds):

TurnAccelMin = 10000.0 TurnAccelMax = 2000.0 TurnDelta = 1000.0 

Note that acceleration is based on the sample rate so a lower maximum results in more samples over time. Even though sampling is in milliseconds, acceleration is stored as microseconds to account for a finer delta.

I would like to graph this so that I can visually see how the delta affects the acceleration over time. While I can picture in my mind the linear acceleration, I want to graph this so that I can visualize how different kinds of acceleration (exponential, quadratic, etc.) affect acceleration over a sample period.

How can I graph this as a line given these values as an equation?

Currently (as linear), where x = Time between 0 and 5 seconds and y = Acceleration in milliseconds.

Ideally I would like to see a graph of points, each connected by a straight line, as well as a table of values for each point when it is polled.

Nested Loop has very low estimates due to skewed data

On SQL Server 2016 SP2 we have a query that has a very low estimate on the nested loop operator. Due to the low estimate this query also spills to tempdb.

If I’m correct SQL Server 2014+ uses Coarse Histogram Estimation to calculate the estimated number of rows on a join. But when I execute the query, SQL Server uses the density vector to calculate the number of estimated rows. Is SQL Server only using the Coarse Histogram Estimation if there is no where clause?

Normally I would use filtered statistics to improve estimations when I have a table with skewed data. But in this case that doesn’t seem to work.

Is there a way to improve the estimations on the nested loop?

Using following code you can reproduce the data:

create table MyTable (     id int identity,     field varchar(50),     constraint  pk_id primary  key clustered (id) ) go  create table SkewedTable (     id int identity,     startdate datetime,     myTableId int,     remark varchar(50),     constraint  pk_id primary  key clustered (id) )  set nocount on  insert into MyTable select top 1000 [name] from master..spt_values go  insert into SkewedTable select GETDATE(),FLOOR(RAND()*(1000))+1,REPLICATE(N'A',FLOOR(RAND()*(40))+1) go 1000  insert into SkewedTable select GETDATE(),FLOOR(RAND()*(1000))+1,REPLICATE(N'A',FLOOR(RAND()*(40))+1) go   CREATE NONCLUSTERED INDEX [ix_field] ON [dbo].[MyTable]([field] ASC) go  CREATE NONCLUSTERED INDEX [ix_mytableid] ON [dbo].[SkewedTable]([myTableId] ASC) go  --95=varchar in sys.messages set nocount off  ;with cte as (      select GETDATE() as startdate ,95 as myTableId, REPLICATE(N'B',FLOOR(RAND()*(40))+1) as remark     union all     select * from cte ) insert into skewedtable select top 40000 * from cte option(maxrecursion 0) go  update statistics mytable with fullscan go  update statistics skewedtable with fullscan go 

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