A quantity increases in a manner such that the ratio of its values in any two consecutive
years is constant. If the quantity doubles every 6 years, by what factor
does it increase in two years?
Can someone provide a simple solution?
exponential growth
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Here is a formula for exponential growth:aishwarya garg wrote:A quantity increases in a manner such that the ratio of its values in any two consecutive
years is constant. If the quantity doubles every 6 years, by what factor
does it increase in two years?
Can someone provide a simple solution?
Final amount = original amount * multiplier^(number of changes).
Plug the following values into the formula above:
Original amount = 1.
Final amount = 2. (Since every 6 years the original amount doubles.)
Multiplier = x. (The factor by which the original amount will be multiplied every 2 years.)
Number of changes = 3. (Since over 6 years the original amount will be multiplied by x three times.)
2 = 1 * x^3
x = 2^(1/3).
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Hi Aishwarya,
Such a series is called Geometric Progression
If you think about the terms in standard for considering a as First term and r as common ratio then terms will be
1st Term -- in Start of the year year --- a
2nd Term -- after 1 year --- ar
3rd Term -- after 2 year --- ar^2
4th Term -- after 3 year --- ar^3
5th Term -- after 4 year --- ar^4
6th Term -- after 5 year --- ar^5
7th Term -- after 6 year --- ar^6
As per the condition given
ar^6 = 2a [the sum become double in six years]
Therefore r^6 = 2
But the factor by which the sum changes in 2 years
ar^2/a = r^2 = Cube Root (r^6) = Cube root of 2 = 2^(1/3)
Such a series is called Geometric Progression
If you think about the terms in standard for considering a as First term and r as common ratio then terms will be
1st Term -- in Start of the year year --- a
2nd Term -- after 1 year --- ar
3rd Term -- after 2 year --- ar^2
4th Term -- after 3 year --- ar^3
5th Term -- after 4 year --- ar^4
6th Term -- after 5 year --- ar^5
7th Term -- after 6 year --- ar^6
As per the condition given
ar^6 = 2a [the sum become double in six years]
Therefore r^6 = 2
But the factor by which the sum changes in 2 years
ar^2/a = r^2 = Cube Root (r^6) = Cube root of 2 = 2^(1/3)
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You can read more about the progressions from the links given below
https://www.beatthegmat.com/mba/2009/09/ ... th-section
https://www.questionbank.4gmat.com/mba_p ... 0504.shtml
https://www.beatthegmat.com/mba/2009/09/ ... th-section
https://www.questionbank.4gmat.com/mba_p ... 0504.shtml
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