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

r ≈ 26%

`W_(t)  = 85* 2^{(t)/(3) }`

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* 2^{(t)/(3) }` ........ (1)

Therefore, for t = 1 year,

`W_(1)  = 85 * 2^{(1)/(3) } = 107.09` thousand megawatts.

Again, for t = 2 years,

`W_(2) = 85 * 2^{(2)/(3) } = 134.93` thousand megawatts.

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

`W_(2) = W_(1)(1 + (r)/(100)) ^(1)`

⇒
`134.93 = 107.09(1 + (r)/(100)) ^(1)`

⇒ r = 25.99% ≈ 26% (Answer)