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

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1. Isaiah.Feynman

A geometric sequence it seems.

2. anonymous

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

3. anonymous

@dtaylor417

4. Isaiah.Feynman

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

5. anonymous

ok man, thanks ill see if it works out

6. anonymous

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)

7. anonymous

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