Stephan earns a base salary of $500 per month plus 10% commission for his monthly sales. If his commission rate is doubled, will his earnings also double?

No. An equation for how much he earns could be written as P=500+0.1x with x being his monthly sales, and P being his profit. If P=500+0.2x, this is only double when two times the first equation equals the second equation.

2 (500+0.1x) = 500+0.2x

1000+0.2x=500+0.2x

500=0

So his earnings are only double when $500 is equal to $0 which makes no sense, so his earnings will not be doubled.

No. The 10% commission will double to 20%,

but the base salary of $500 won't change.