The size of bacteria triples every 12 years. If the piece of bacteria was 25mm in 1990, within what year will the bacteria be 129 mm in size.
Options are: 2000, 2002, 2008, and 2014
show work please

Question

The size of bacteria triples every 12 years. If the piece of bacteria was 25mm in 1990, within what year will the bacteria be 129 mm in size. 
Options are: 2000, 2002, 2008, and 2014
show work please

anonymous · Answer

define: bacteria grows according to the function g(k) = a*3^(k/12) where a is initial length and k is number of years since bacteria was at initial length.
we solve for 129 = 25*3^(k/12) ; k = 17.9 approx = 18 years after it was 25 mm long. Thus the answer is 1990 +18 = 2008