GDP per-capita

Let y-GDP per-capita, x=GDP per-worker, and z-share of workers in the population (i.e. Workers/Population).A. Mathematically prove that y must equal the product of x times z.B. Given that y x*z, how are the growth rates of x, y, and z related? (No need to formally prove this, though you can if you’d like. It is easier to use a growth rule from our class or a math class, but state the rule in words or equations before using it)C. Since the share of workers in an economy is bounded between zero and one, it can’t grow or shrink forever. Hence, if z is constant in the long-run, what does that imply about the lon-run relationship between growth rates of GDP per-capita and GDP per-worker?