anonymous
  • anonymous
A culture started with 5000 bacteria. After 5 hours, it grew to 6500 bacteria. Predict how many bacteria will be present after 16 hours. Round your answer to the nearest whole number. P=Ae^kt
Mathematics
jamiebookeater
  • jamiebookeater
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donnie1999
  • donnie1999
Hey beautiful :D
anonymous
  • anonymous
@donnie1999 hello ^.^
butterflydreamer
  • butterflydreamer
The culture originally started with 5000 bacteria. This means: \[t = 0 , P = 5000\] Sub that into your equation "P=Ae^kt" to find A

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butterflydreamer
  • butterflydreamer
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butterflydreamer
  • butterflydreamer
So we now know that A = 5000, so we can add that to our formula: \[P = Ae ^{kt} \rightarrow P = 5000e ^{kt}\] Next, we're told that "After 5 hours, it grew to 6500 bacteria" So when \[t = 5, P = 6500\] Plug these into your formula and work out what "k" equals to. \[P = 5000e ^{kt} \rightarrow 6500 = 5000e ^{5k}\] Solve for "k"
butterflydreamer
  • butterflydreamer
k = ?
butterflydreamer
  • butterflydreamer
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butterflydreamer
  • butterflydreamer
now we know the values of the following A = 5000, k= 1/5*ln(13/10) and t=16, so find P

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