Answer:
The doubling time is 10.7 years after 1975 i.e. on 1986.
Step-by-step explanation:
In 1975, the value of the index was set at 1000. Since then, the value can be modeled as
[tex]I = 1000(2)^{\frac{n}{10.7}} = 1000(2)^{0.0934n}[/tex] ............. (1)
where n is number of years since 1975.
Now, we asked to calculate the doubling time of the index.
So, [tex]2000 = 1000(2)^{0.0934n}[/tex]
⇒ [tex]2 = (2)^{0.0934n}[/tex]
⇒ 0.0934n = 1
⇒ n = 10.7 years
Therefore, the doubling time is 10.7 years after 1975 i.e. on 1986. (Answer)
