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If I want a number x to grow to the number y over z periods, how do I compute my growth rate per period? So assume x = 10, and y = 80 and z = 3, then I would have a growth rate of 100% every period:

  • 10
  • 20 (1st period)
  • 40 (2nd period)
  • 80 (3rd period)

How to compute that growth rate?

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    Ah, you are right.2012-09-27

1 Answers 1

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It's easier to think of growth factor at first: So your number is multiplied by $g$ at each step. After $z$ steps, it is multiplied by $g^z$, so you end up with an equation $g^zx=y$ to be solved for $g$. To do that, take logarithms and end up with a linear equation for $\log g$.

Afterwards, you convert your $g$ to a growth rate $g-1$. Multiply by 100 if you want it as a percentage.

In your example, the equation is $g^3\cdot10=80,$ i.e., $g^3=8$. You hardly need logs to do that one, but if you do, logarithms with base 2 can't be beat: $3\log_2 g=\log_28=3$, so $\log_2g=1$, and $g=2^1=2$.

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    @HaraldHanche-Olsen: I wrote the formula correct, but the approach to solve is exactly you gave in your answer. Here, taking $z^{th}$ root was simple, but in general first you have to first compute $\log g$ using $\log$ tables and then compute $anti-log$ of $\log g$ to get $g$2012-09-27