suppose that one bacterial cell divides every 30 minutes to make 2 cells. write an expression to find how many cells there will be after 3 hours. then solve to find the total number of cells after 3 hours.
with time in hours, starting with one cell, after t hours, the population p will be
p(t) = 2^(2t)
p(3) = 2^6 = 64
12 cells
To find the expression for the number of cells after a given time, we need to determine the number of divisions that occur within that time period.
Since one bacterial cell divides every 30 minutes to form 2 cells, we can calculate the number of divisions in 3 hours, or 180 minutes, by dividing the total time period by the division time:
Number of divisions = 180 minutes ÷ 30 minutes/division = 6 divisions
Now, to find the total number of cells after 3 hours, we need to calculate 2 to the power of the number of divisions, as each division results in the formation of 2 cells.
Let's denote the number of cells after 3 hours as "N". The expression to calculate the total number of cells can be written as:
N = 2^number of divisions
Solving this expression using the values we calculated, we have:
N = 2^6 = 64 cells
Therefore, after 3 hours, there will be a total of 64 bacterial cells.