Brock is a plumber. He charges a flat rate of $40 to visit a house to inspect its plumbing. He charges an additional $20 for eve
ry hour he spends inspecting or making repairs which graph below correctly shows the price of using brocks plumbing service vs time?
A) graph W
B) graph X
C) graph Y
D) graph Z
A) graph W
B) graph X
C) graph Y
D) graph Z
1 answer:
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If 
is an integer, you can use induction. First show the inequality holds for 
. You have 
, which is true.
Now assume this holds in general for
, i.e. that 
. We want to prove the statement then must hold for 
.
Because, you have
and this must be greater than
for the statement to be true, so we require
for
. Well this is obviously true, because solving the inequality gives 
. So you're done.
If you is any real number, you can use derivatives to show that 
increases monotonically and faster than .
Now assume this holds in general for
Because
and this must be greater than
for
If you
You can perform all kind of operation that are one the inverse of the other, so that the value won't change. For example, you can multiply and divide by 2:
Or add and subtract 5: