anonymous
  • anonymous
A bacteria culture starts with 1,500 bacteria and doubles in size every 4 hours. Find an exponential model for the size of the culture as a function of time t in hours
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
a(t)=Ae^rt
anonymous
  • anonymous
3000=1500e^4r
anonymous
  • anonymous
ln2=4r

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anonymous
  • anonymous
t=ln2/4
anonymous
  • anonymous
a(t)=Ae^(ln2)t/4
anonymous
  • anonymous
sry... r = (ln2)/4 the last answer is still correct
anonymous
  • anonymous
Valpey, what do you think?
anonymous
  • anonymous
P = Noe^(kt) where P is amount after t time No is the initial amount . No is 1500 bacteria doubles in size every 4 hours so when t=4, P = 3000 3000 = 1500e^(4k) 2= e^(4k) ln(2) = 4k ln(2)/4 = k 0.17328679513999 =k so k=0.1733 P = 1500e^(0.1733t) so required equation is . F(t) = 1000e(0.34657t)
anonymous
  • anonymous
initially its 1500 after 4hrs it becomes 1500*2 after 8 hrs----> 1500*2^2 after 12hrs---->1500*2^3 . . . after 4*t hrs---->1500*2^t so after t hrs its given by \[1500*2^t/4\]

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