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October 12th, 2018, 12:37 PM   #1
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Is There A Proof That This Function Decreases?

I don't know what type of math it requires, but calculus includes rates of change so I posted it here. The rule of 70 states that 70 divided by the percent increase per period will estimate the amount of periods it will take money to double. I entered multiples of 0.1% into Excel from 0.1% through 10%. Then I took the amount to the exponent of (70/the % increase) to calculate the ratio. For example, a 0.1% increase for 700 periods multiplies amounts by about 2.013. As the percents increased from 0.1% to 10%, the amount increased at a decreasing rate. Is there a proof that this function decreases? The percent increase that the rule of 70 would make the amount double is between 1.9% and 2.0%. At percent increases higher than that, the formula gives values less than 2.
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October 13th, 2018, 09:21 AM   #2
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If it helps, the function is y = (1 + x/100)^(70/x).
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October 13th, 2018, 10:20 AM   #3
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Using derivatives wont show if it decreases , i have no idea for the moment (maybe later i can find)
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