A math question for debate

[vincent1]

I came across this question:
If A increases by 35%, then B increases by 25%. Given that A increases 1%, find the percentage increase of B. How would you interpret the question? What's your answer?
Thanks in advance.

 

[Deleted member 4993]

I came across this question:
If A increases by 35%, then B increases by 25%. Given that A increases 1%, find the percentage increase of B. How would you interpret the question? What's your answer?
Thanks in advance.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[vincent1]

I came across this question:

If A increases by 35%, then B increases by 25%. Given that A increases 1%, find the percentage increase of B.

Here is 1 possible solution

Assumed (B1/B0) = (A1/A0)^k , ( this is sort of like compound interest, with 1.35 maps to 1.25, 1.35^2 maps to 1.25^2. So k is (log1.25/log1.35).

sub in (A1/A0)=1.01 to obtain (B1/B0).

Here is another suggested solution,

Assume (deltaB/B0) = k (deltaA/A0), ( this is sort of like return on investing a certain portion of your money), 35% maps to 25%, and 7% maps to 5%, so k=5/7.

There was a suggestion on letting B=f(A), then 1.25f(A)=f(1.35A) , 1.25^n f(A) =f(1.35^n A), for integral values n.


Can you analysis which method is appropriate and effective, and what implicit assumptions are made in each method.



Thanks in advance.