Answer:
r ≈ 26%
[tex]W_{t} = 85\times 2^{\frac{t}{3} }[/tex]
Step-by-step explanation:
Total power generated by wind worldwide doubles every 3 years.
In a particular year, the world wind generating capacity was 85 thousand megawatts.
So, the formula for wind generating capacity W (in thousand megawatts) as a function of t. the number of years in the future will be given by
[tex]W_{t} = 85\times 2^{\frac{t}{3} }[/tex] ........ (1)
Therefore, for t = 1 year,
[tex]W_{1} = 85 \times 2^{\frac{1}{3} } = 107.09[/tex] thousand megawatts.
Again, for t = 2 years,
[tex]W_{2} = 85 \times 2^{\frac{2}{3} } = 134.93[/tex] thousand megawatts.
As the continuous growth rate is exponential, so, we can write
[tex]W_{2} = W_{1}(1 + \frac{r}{100}) ^{1}[/tex]
⇒ [tex]134.93 = 107.09(1 + \frac{r}{100}) ^{1}[/tex]
⇒ r = 25.99% ≈ 26% (Answer)
