Is worsening wealth inequality intrinsic to Capitalism? I am but a humble lay person, but I have a question.

I've been thinking about wealth inequality and the structure of capitalism. It seems to me that the pay rate for workers accumulates in a linear way. That is, during year 1 you make X, at the end of year 2 you've made 2X, at year 3 you've accumulated 3X and so on. You may get raises (although probably not so much in our current economic conditions of a labor oversupply) or switch jobs, but if you stayed at the same firm, and conditions didn't change much, then your savings accumulate in a linear way.

But for the business who hires you, they start out with some money, then they use that money to buy raw materials and pay you to convert them into a product, then they take your finished product and sell it for more money than they started with. Let's say they start off with Y, then at the end of a year they have 2Y. But this is an exponential growth: they then start over the process using their 2Y, and can hire twice as many people and buy twice as much raw materials and sell twice as much, to end up with 4Y at the end. 

So while worker worth goes up in a linear way, 1X, 2X, 3X, 4X...the employer's worth goes up in an exponential way, 1Y, 2Y, 4Y, 8Y...So in that case, isn't wealth inequality fundamentally built right into capitalism, and therefore we should expect it to pretty much always get worse as time goes on, unless measures are taken to combat or reverse it after the fact? Am I wrong in my analysis here?
While the owners of a successful business will generally experience an exponential growth compared to their employees, there are some factors to consider:


I find it unrealistic for any business to maintain a growth rate of 100% over many years. (As per the example) You can only sell twice as much if you can find twice as many buyers.
As a business grows, it is likely to start hiring more people and paying them better as they need better skills.
The business also takes the risk. The worker is generally guaranteed his X, but stockholders may have to expect the occasional decline in profit, or even a loss. The company may even go out of business in which case they cannot recover much, if any, of their investment. Those who take the risks, get the reward. Businesses failing also mean that bad investors can often lose fortunes, it's not always a good investment.
There is nothing stopping the employee from owning part of the company by investing in some shares. Then he too may experience this exponential growth. He must also keep in mind, however, that he must now also accept the risks of such an investment.