SOLUTION: Ethanol production (in billions) of gallons) is produced by f(x) = 1.47(1.225^x) where 0 corresponds to 2000. If this trend continues, estimate the year in which ethanol productio

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Question 171462This question is from textbook finite math with application
: Ethanol production (in billions) of gallons) is produced by f(x) = 1.47(1.225^x) where 0 corresponds to 2000. If this trend continues, estimate the year in which ethanol production reaches 12 billion gallons. This question is from textbook finite math with application

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Ethanol production (in billions) of gallons) is produced by f(x) = 1.47(1.225^x) where 0 corresponds to 2000. If this trend continues, estimate the year in which ethanol production reaches 12 billion gallons.
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12x10^9 = 1.47(1.225^x)
1.225^x = [12x10^9]/1.47
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Take the log of both sides:
x[log1.225] = [log(12x10^9] - [log1.47]
x = [10.07918-0.167317335]/[0.088136089] = 112.46 yrs
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2000+112.46 is the year 2113
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Cheers,
Stan H.