Tissue Engineering Problem - Find minimum starting cell population

[bmed90]

Homework Statement

You want to create a tissue engineered blood vessel using smooth muscle cells. Your plan is to isolate smooth muscle cells from discarded human tissue obtained from heart surgery and grow them for a long time to create cells own ECM. Smooth muscle cells have enormous groth potential in culture and assume they have a doubling time of 15 hours. If you need at least 5 trillion cells to make the blood vessel in four weeks what minimum starting cell population would you need?

Homework Equations

The Attempt at a Solution

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I've tried several attempts and I don't think they are even worth posting. Cant seem to get reasonable answers.

 

[Borek]

This is about exponential growth. It will be probably easier to find information about exponential decay, but the math is the same, just works in a different direction.

 

[epenguin]

Everyone should understand exponentials but this is a biologist in a hurry.

According to Wikipedia a trillion can mean either 10¹² or 10¹⁸ which is not a negligible difference. So use scientific notation please.

The cell population doubles in 15 hours. So if it's a trillion (whatever that is) now, it was half a trillion 15 hours ago. It halves every 15h you go back in time. So how many halving times, how many 15 h are there in 4 weeks? So the number of cells you needed to start with is (a trillion) X (1/2)^ raised to the power of that number of halving times. In other words you multiply by a half for every 15 h.

What was unreasonable about the answers you got? Was it less than one? Doesn't mean the maths was wrong. What does it mean?

 

[bmed90]

Everyone should understand exponentials but this is a biologist in a hurry.

According to Wikipedia a trillion can mean either 10¹² or 10¹⁸ which is not a negligible difference. So use scientific notation please.

The cell population doubles in 15 hours. So if it's a trillion (whatever that is) now, it was half a trillion 15 hours ago. It halves every 15h you go back in time. So how many halving times, how many 15 h are there in 4 weeks? So the number of cells you needed to start with is (a trillion) X (1/2)^ raised to the power of that number of halving times. In other words you multiply by a half for every 15 h.

What was unreasonable about the answers you got? Was it less than one? Doesn't mean the maths was wrong. What does it mean?

Well honestly I can tell you right now that whatever I got was wrong. I got like 5.6e11... So your saying the answer is 1e12(.5)^44

 

[Borek]

So your saying the answer is 1e12(.5)^44

44.8 to be precise.

 

[epenguin]

Well honestly I can tell you right now that whatever I got was wrong. I got like 5.6e11... So your saying the answer is 1e12(.5)^44

Yes. Which is...?