Total power generated by wind worldwide doubles every 3 years. In a particular year, the world wind-generating capacity was abou
t 94 thousand megawatts. Find the continuous growth rate and give a formula for wind generating capacity W W (in thousand megawatts) as a function of t t , the number of years in the future.
<span>f(t) = 94*1.25992105^t
Since the value doubles every three years we want an X such that
X^3 = 2
Or in simpler terms, our growth rate is the cube root of 2. So lets get that. To calculate the nth root of a number you can take the logarithm of the number, divide by n, then get the anti-log. So
10^(log(2)/3) = 10^(0.301029996/3) = 10^0.100343332 = 1.25992105
Now the function becomes trivial. I'll use t as the number of years since the baseline capacity was calculated (94 thousand megawatts at t = 0). So
f(t) = 94*1.25992105^t</span>
