SOLUTION: 2. A cell divides into two identical copies every 4 minutes. How many cells will exist after 3 hours?

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Question 155383: 2. A cell divides into two identical copies every 4 minutes. How many cells will exist after 3 hours?
Answer by jim_thompson5910(28715) About Me  (Show Source):
You can put this solution on YOUR website!
A=A%5B0%5De%5E%28kt%29 Start with the general exponential function


2A%5B0%5D=A%5B0%5De%5E%28k4%29 Plug in t=4 and A=2A%5B0%5D (since the number of cells double every 4 minutes)


2=e%5E%284k%29 Divide both sides by A%5B0%5D


ln%282%29=4k Take the natural log of both sides.


0.69315=4k Take the natural log of 2 to get 0.69315.


0.17329=k Divide both sides by 4


So the growth/decay constant is k=0.17329


A=A%5B0%5De%5E%28kt%29 Go back to the general exponential function


A=%281%29e%5E%280.17329%2A180%29 Plug in A%5B0%5D=1 (since we start from one cell), k=0.173, and t=180 (note 180 minutes = 3 hours)


A=%281%29e%5E%2831.1922%29 Multiply 0.17329 and 180 to get 31.1922


A=%281%29%283.52%2A10%5E%2813%29%29 Raise "e" to the 31.1922 power to get 3.52%2A10%5E%2813%29


A=3.52%2A10%5E%2813%29 Multiply


So after 3 hours, there are approximately 3.52%2A10%5E%2813%29 cells which is about 35.2 trillion cells