At the beginning of an experiment a colony has N bacteria. Two hours later it has 4N bacteria. How many hours, measured from the beginning, does it take for the colony to have 10N bacteria.

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- May 5th 2010, 08:14 AMryan18bacteria problem
At the beginning of an experiment a colony has N bacteria. Two hours later it has 4N bacteria. How many hours, measured from the beginning, does it take for the colony to have 10N bacteria.

- May 5th 2010, 08:59 AMAllanCuz
The equation for bacteria growth comes from

Which is a well known seperable equation. In this case, I imagine you don't need to derive the equation so we'll skip right to it.

We are going to use

where we let t be time in hours.

At time 0 we have N bacteria so the above equation stays the same.

At time 2 we have 4N bacteria so we can find K,

Now, we sub back into our first equation to get.

At what time t does the colonie have 10 bacteria?

- May 5th 2010, 09:57 AMSoroban
Hello, ryan18!

Quote:

At the beginning of an experiment a colony has bacteria.

Two hours later, it has bacteria.

How many hours, measured from the beginning,

. . does it take for the colony to have bacteria?

The general population function is: .

When

. . We have: .

When

. .

The function is: .

If , we have: .

Take logs: .

. .