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Find all functions f:R -> R such that:
f(floor(x)*y) = f(x)*floor(f(y)) holds for all x and y.

Prove that no other function satisfies the above relationship.

(No Solution Yet, 0 Comments) Submitted on 2016-09-30 by K Sengupta   
Difficulty: 3 of 5 Bonus: The Rule of 72 (in Just Math) Rating: 3.67
The Rule of 72 is a rule of thumb that states that the number of time periods (such as years) that it takes for a sum to double at compound interest is very nearly 72 divided by the percentage interest rate per period. Thus, for example, it takes (almost exactly) 9 years for a sum to double at 8% interest compounded yearly.

1. Using the rule, find the annual rate of increase for an investment that has quadrupled in 24 years. Compare to the exact value.

2. At what interest rate is the rule exact?

3. Justify the rule using mathematical analysis and a few numerical calculations.

(Solution Posted, 6 Comments) Submitted on 2005-01-25 by Richard   
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Difficulty: 3 of 5Find Function From Fraction (in Just Math)
Posted on 2016-09-22 by K Sengupta (No Solution Yet, 3 Comments)

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