SOLUTION: in a country the wind power capacity has grown exponentially from 4766 megawatts in 2002 to 46,911 megawatts in 2012. find the exponential growth rate k and write an equation for a
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Question 1162868: in a country the wind power capacity has grown exponentially from 4766 megawatts in 2002 to 46,911 megawatts in 2012. find the exponential growth rate k and write an equation for an exponential function that can be used to predict the wind power in megawatts, t years after 2002. Estimate the year in which wind power capacity will reach 120,000 megawatts.
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52866) (Show Source): You can put this solution on YOUR website!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If 2002 is year 0, then 2012 is year 10.
We need a function of the form \ =\ ae^{kt})
Where 
is the year zero value (because 
) and 
is the growth rate per year since 2002, and 
is the year since 2002.
We are given that \ =\ 4766)
, so
\ =\ 4766e^{k(0)})
Then we are given that \ =\ 46911)
, so
)
\,-\,\ln(4766)}{10})
Do the arithmetic indicated to find the approximate value of , then use that value in:
and solve for
Sometime in the first couple of weeks of February 2016.
John
My calculator said it, I believe it, that settles it
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