Question 1100000: In a country, the wind-power capacity has grown exponentially from 4383 megawatts in 2001 to 46,908 megawatts in 2011.
a) Find the exponential growth rate k and write an equation for an exponential function that can be used to predict the wind-power capacity, in megawatts, t years after 2001.
b) Estimate the year in which wind-power capacity will reach 110,000 megawatts
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! a)Let P(0) be the initial amount of megawatts available in 2001. Then the amount of megawatts available in t years after 2001 would be:
P(t)=P(0)*e^rt, where r is the constant rate of growth.
b)From the problem described above:
P(10)=4383*e^10r
46908=4383*e^10r
10.702258726899383983572895277207=e^10r
ln 10.702258726899383983572895277207=ln e^10r=10r ln e=10r
r=0.23704548151621459459063636092045
Then:
110,000=4383*e^0.23704548151621459459063636092045t
25.096965548710928587725302304358=e^0.23704548151621459459063636092045t
ln 25.096965548710928587725302304358=ln e^0.23704548151621459459063636092045t=0.23704548151621459459063636092045t ln e=0.23704548151621459459063636092045t
t=13.595479330557494389544573916097 years after 2001, or about halfway into 2014
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