Question

Total power generated by wind worldwide doubles every 3 years. In a particular year, the world wind generating capacity was about 86 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.

The continuous growth rate is ______ percent.

W =

Answer 1

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

tada