Question

Question #46f24

Answer 1

The original year and value are almost irrelevant to the answer. Percentage is about proportion, which will only be determined by the factor `1.009^((2/3)x)`.

Notice that

`1.006^3 = (1.0 + 0.006)^3`

`= 1.0 + (3xx0.006) + (3xx0.006^2) + 0.006^3`

`= 1.0 + 0.018 + 0.000108 + 0.000000216`

`= 1.018108216`

And that

`1.009^2 = (1.0 + 0.009)^2`

`= 1.0 + 0.018 + 0.000081`

`= 1.018081`

So `1.009^2 ~= 1.006^3` and `1.009^(2/3) ~= 1.006`.

`1.009^((2/3)x) = (1.009^(2/3))^x ~= 1.006^x`

Multiplying by `1.006` is the same as adding `0.6`%