SOLUTION: express the problem as an exponential function whose value is the number of cells after x divisions, and then use the function to determine the answer. A cell divides into two i

Algebra ->  Equations -> SOLUTION: express the problem as an exponential function whose value is the number of cells after x divisions, and then use the function to determine the answer. A cell divides into two i      Log On


   

Question 194842This question is from textbook
: express the problem as an exponential function whose value is the number of cells after x divisions, and then use the function to determine the answer.
A cell divides into two identical copies every 4 minutes. How many cells will exist after 5 hours? Thank You This question is from textbook

Found 2 solutions by checkley77, josmiceli:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
2^(5*60)/4=2^(300/4)=2^75=3.7779*10^22

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Make a chart:
# of divisions --- # of copies ------- # of minutes
--- 0 ---------------- 1 ------------------- 0
--- 1 ---------------- 2 ------------------- 4
--- 2 ---------------- 2+4= 6 -------------- 8
--- 3 ---------------- 2+4+12= 18 ---------- 12
--- 4 ---------------- 2+4+12+36= 54 ------- 16
--- 5 ---------------- 2+4+12+36+108= 162 -- 20
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I think I have a formula that works.
If x= the number of divisions,
then the number of copies of cells
=2%2A3%5E%28x-1%29, since
2%2A3%5E%281-1%29+=+2
2%2A3%5E%282-1%29+=+6
2%2A3%5E%283-1%29+=+18
2%2A3%5E%284-1%29+=+54
2%2A3%5E%285-1%29+=+162
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How many cells will exist after 5 hours?
Let C= the number of copies after x
5%2A60+=+300 min in 5 hrs
300%2F4+=+75
75 times in 3 hrs divisions will occur
This method deals with all but the very 1st cell.
I can correct for that by adding in 2%5Ex
------------------------------------------------
C%2875%29+=+2%2A3%5E%2875-1%29+%2B+2%5E75
C%2875%29+=+2%2A3%5E74+%2B+2%5E75
C%2875%29+=+405.511%2A10%5E33+%2B+37.779%2A10%5E21
C%2875%29+=+10%5E21%2A%28405.511%2A10%5E12+%2B+37.779%29
The approximate answer is
C%2875%29+=+4.055%2A10%5E35
and hopefully it's right