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

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> 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      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

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(48535) 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.
-----------------
12x10^9 = 1.47(1.225^x)
1.225^x = [12x10^9]/1.47
-----
Take the log of both sides:
x[log1.225] = [log(12x10^9] - [log1.47]
x = [10.07918-0.167317335]/[0.088136089] = 112.46 yrs
---------------
2000+112.46 is the year 2113
==================================
Cheers,
Stan H.