Hi, there. I'm happy to help!
First of all, let's consider the revenues. "
in 2009 its revenues were 44% higher than in 2007." That's a 44% increase, which means
(2009 rev) = 1.44*(2007 rev)
Well, if we assume a constant rate of growth, a constant percentage, that means the multiplier would be constant each year
(2008 rev) = r*(2007 rev)
(2009 rev) = r*(2008 rev) = (r^2)*(2007 rev)
BIG IDEA: to figure out the single year percent increase from multiple years, you don't take a root of the multi-year percentage, but rather a root of the multi-year muliplier.
r^2 = 1.44
r = 1.2
So the revenue grows 20% a year. That means costs grow at 10% a year.
We know it operated at a $1000 loss in 2007, which means (2007 rev) = (2007 costs) - 1000
(2008 cost) = (2008 rev)
1.1*(2007 cos) = 1.2(2007 rev)
1.1*(2007 cos) = 1.2[(2007 costs) - 1000]
1.1*x = 1.2*(x - 1000)
1.1x = 1.2x - 1200
1200 = 0.1x
12000 = x
The cost in 2007 were $12,000.
The cost in 2008 were 10% greater, #13,200, which were also the revenue in 2008.
Cost in 2009 = 13200*1.1 = 14,520
Revenue in 2009 = 13200*1.2 = 15,840
(2009 profit) = (2009 rev) - (2009 cost)
= 15840 - 14520 = $1320
Hmm. This is close to C, but not exact. I was interpreting growth as a percent growth, and "twice as fast" as double the percent, but now I wonder if that's what the author of the question had in mind. If it's not, then I would argue the question is not clearly written.
I hope that's helpful. Let me know if you have any further questions.
Mike
