Total power generated by wind worldwide doubles every 3 years. In a particular year, the world wind-generating capacity was about 85 thousand megawatts. Find the continuous growth rate and give a formula for wind generating capacity W (in thousand megawatts) as a function of t, the number of years in the future.

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)