<p>hey guys im having a tough time trying to figure out this problem.
the number of cells in a certain population doubles every 30 minutes. if the population starts with 1 cell, which of the following gives the total number of cells in the population after n hours? (assume n is a positive integer)</p>
<p>A. (2n)/60
B. 2n
C. n^2
D. 2^n
E. 2^2n</p>
<p>the correct answer is E.... but why?</p>
<p>every 30 minutes it doubles:
0 minute = 1 cell
30 minutes = 2 cells
60 minutes = 4 cells
90 minutes = 8 cells
120 minutes = 16 cells</p>
<p>n = # of hours = 60 minutes</p>
<p>2^2n…refer to the above table:
when n = 0 there is 1 cell, 2^0 is 1
when n = 1 there are 4 cells, 2^2 is 4
when n = 2 there are 16 cells, 2^4 is 16</p>
<hr>
<p>you could also realize that since n is 60 minutes, 2 times greater than 30 minutes, the amount of those sessions (compared to the 30-minute sessions) is halved. So in 4 30-minute sessions you get 2 hour sessions. So you would have to multiply n by 2 and use that as the number of 30-minute sessions.</p>
<p>So 2^2n is essentially saying the rate (2, because the population doubles every session) to the number of sessions power. Basically 2<em>2</em>2<em>2</em>2 where the number of 2s is the number of 30-minute sessions that have passed. This quantity defines how the population multiplies.</p>
<p>So you multiply this quantity with the initial quantity (1) to get the final quantity after n hours, or 2n 30-minutes
1<em>2^2n, or simply 2^2n
So if the population started with 3, you would do (3)</em>(2^2n)</p>