Question

The U.S annual production of ethanol, used as fuel for automobiles, was6.5 billion gallons in 2007 and has grown by about 26% per yearthen. predict when annual ethanol will reach 33 billion gallons.

Answer 1

\[6.5\times (1.26)^t=33\] is what you need to solve

Answer 2

make sure you add whatever you get for t to 2007 to get the right year...remember it doesnt start at year = 2000

Answer 3

so how would i start it??/

Answer 4

first step is to divide by \(6.5\) to get
\[(1.26)^t=\frac{33}{6.5}\] then change of base to get
\[t=\frac{\ln(\frac{33}{6.5})}{\ln(1.26)}\]
then a nice calculator

Answer 5

so ones i get the answer is there anything else i have to do or is that just it. because in the back of the book the answer is in the year 2014

Answer 6

yes. t is the amount of time (in years) it takes (approx 7.02 years). You have to add this to the amount of time that already passed (given as 2007) to get 2007+7=2014

Answer 7

ok thanks a lot.