Question

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 1

Answer:

r ≈ 26%

$W_{t} = 85\times 2^{\frac{t}{3} }$

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  

$W_{t} = 85\times 2^{\frac{t}{3} }$ ........ (1)

Therefore, for t = 1 year,

$W_{1} = 85 \times 2^{\frac{1}{3} } = 107.09$ thousand megawatts.

Again, for t = 2 years,

$W_{2} = 85 \times 2^{\frac{2}{3} } = 134.93$ thousand megawatts.

As the continuous growth rate is exponential, so, we can write

$W_{2} = W_{1}(1 + \frac{r}{100}) ^{1}$

⇒ $134.93 = 107.09(1 + \frac{r}{100}) ^{1}$

⇒ r = 25.99% ≈ 26% (Answer)