Question

In 1975, the value of the index was set at 1000. Since then, the value can be modelled as I=1000(2)^n/10.7, where n is number of years since 1975. On average, what is the 'doubling time'?

Answer 1

The doubling time is 10.7 years after 1975 i.e. on 1986.

Explanation:

In 1975, the value of the index was set at 1000. Since then, the value can be modeled as

`I = 1000(2)^{(n)/(10.7)} = 1000(2)^(0.0934n)` ............. (1)

where n is number of years since 1975.

Now, we asked to calculate the doubling time of the index.

So,
`2000 = 1000(2)^(0.0934n)`

⇒
`2 = (2)^(0.0934n)`

⇒ 0.0934n = 1

⇒ n = 10.7 years

Therefore, the doubling time is 10.7 years after 1975 i.e. on 1986. (Answer)