"increased by a factor of ..."

[divineacclivity]

Cost is expressed by the formula t.b^4. If b is doubled, by what factor has the cost increased?
(A) 2 (B) 6 (C) 8 (D) 16 (E) 1/2

So, if b is doubled, cost becomes 16 times as much.
So, the cost increased to 16 times the original cost.
Or, the cost increased by 15 times the original cost.
So, doesn't it translate to: "The cost has increased by a factor of 15" instead of "16" as in answer choice D???
Where am I wrong with this one? Please help. Thank you in advance.

Source: Manhattan's Equations, Inequalities, and VICs Guide 4th edition, Problem set of chapter-4

-DA

[RonPurewal]

"Increase by a factor of n" is the same as "multiply by n".
(Your 15 involves a difference, not just a multiplier; the word "factor" is associated with multiplication, not with differences.)

[divineacclivity]

"Increase by a factor of n" is the same as "multiply by n".
(Your 15 involves a difference, not just a multiplier; the word "factor" is associated with multiplication, not with differences.)

Got it. Thanks very much for your wonderful explanation as usual.

[divineacclivity]

post105100.html?sid=7ed0a3834eb45428da03c279280a2268#p105100

I don't know how I end up creating two posts for the same question; I didn't mean to do so at all.
I don't recall exactly but the net might've returned me an error page and that's why I must've submitted the question again; (the two posts have been submitted at the difference of a minute as I can see).

Thank you very much for all your help, Ron :)

[tim]

I think it's okay. Thanks for catching that, and let us know if you have any further questions.

[RonPurewal]

The forum servers are admittedly not the fastest-running machines in cyberspace, but, maybe the problem came from pressing the submit/post button more than once. In any event, no big deal.