A lab technician placed a bacterial cell into a vial at 5 am. The cells divide in such a way that the number of cells doubles every 4 mintues. The vial is full one hour later.
How long does it take for the cells to divide to 4096?
I am not to sure how to set up the equation at= aoc^t/p for this and how to solve for the time.
The question I would ask is, "How many divisions (i.e., doublings) must occur to give a total of 4096 cells?". Mathematically, the answer is n in the equation 2^n = 4096.
To see this, consider zero doublings (n=0) gives 2^0=1 cell. One doubling gives 2^1=2 cells; two doublings: 2^2 = 4 cells; three doublings: 2^3 = 8 cells;...n dounlings: 2^n cells.
If you have not yet learned how to solve exponential equations, e.g., 2^n = 4096, guess untill you find the value of n that makes this equation true. I leave the "guess work" up to you.
Finally, per the given information, each doubling requires 4 minutes time. Hence, the time required to obtain 4096 cells, in minutes, is 4n, where n is that determined as per the preceding paragraph.
Hint: The quotient of your answer and 3 is a perfect square.