## anonymous one year ago 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

1. donnie1999

Hey beautiful :D

2. anonymous

@donnie1999 hello ^.^

3. 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

4. butterflydreamer

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5. 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"

6. butterflydreamer

k = ?

7. butterflydreamer

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8. butterflydreamer

now we know the values of the following A = 5000, k= 1/5*ln(13/10) and t=16, so find P