A bacteria culture begins with 8 bacteria which triple in size every week. How many bacteria exist in the culture after 4 weeks?

Question

isaiah.feynman · Answer

A geometric sequence it seems.

anonymous · Answer

i know how to solve it, i just cant figure out how to set up the equation

anonymous · Answer

@dtaylor417

isaiah.feynman · Answer

Well, it looks like a geometric sequence sum. So, the sum of the first n terms of a geometric sequence is given as, $$S_{n} = a_{1}\frac{ 1 - r^{n} }{ 1-r }$$

anonymous · Answer

ok man, thanks ill see if it works out

anonymous · Answer

At t0=0------> no=8
At t1=1week-------> n1=8*3=24 bacteria
At t2------> n2=8*3^2=72 bacteria
At t3= 3 weeks-------> n3=8*3^3=216 bacteria
At t4=4 weeks-----> n4=8*3^4=684 bacteria (That is the answer)

anonymous · Answer

At tn=n weeks-------. n4=8*3^n