Exponential Growth problem

[yuvarajait]

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?

The answer given is cube root of 2.

Could anyone help understanding & solving these type of problems easily. Thanks!

[force5]

consider this

1st term a1.......................................after 6 years or (7th term)= 2a1

7th term = a1r^6

2a1= a1r^6

r= 2^1/6
now this is the difference between one year.
for two years... 2^1/6*2^1/6= 2^1/3

hence the answer should be cube root of 2


hope it helps.....

[6983manish]

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?

The answer given is cube root of 2.

Could anyone help understanding & solving these type of problems easily. Thanks!

Let the quantity at start is x
Let it increased by a multiple of y every year.

After 1 year = xy
After 2 years = xy^2
After 3 years = xy^3
After 4 years = xy^4
After 5 years = xy^5
After 6 years = xy^6

and its given that xy^6 = 2x
y = (2)^1/6

We need to find the ratio after 2 years = xy^2 / x
= y^2
= [(2)^1/6]^2
= (2)^1/3
Hence , the answer would be cube root of 2 i.e.(2)^1/3

[GMATGuruNY]

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?

The answer given is cube root of 2.

Could anyone help understanding & solving these type of problems easily. Thanks!

Here is the formula for exponential growth:

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).