12. If we have only one (1) E. coli bacteria, at I beginning, in 5 hours time how many E.co will have in culture media? a. 1.6times 10^4 b. 3.2times 10^4 c. 6.4times 10^4 d. 8.1times 10^3

To solve this problem, we need to understand the concept of bacterial growth. E. coli bacteria typically divide every 20 minutes under optimal conditions. This means that the number of bacteria doubles approximately every 20 minutes.<br /><br />Given that we start with one E. coli bacterium, we can calculate the number of bacteria after 5 hours using the formula for exponential growth:<br /><br />\[ N = N_0 \times 2^{(t/T)} \]<br /><br />where:<br />- \( N \) is the final number of bacteria,<br />- \( N_0 \) is the initial number of bacteria (which is 1 in this case),<br />- \( t \) is the total time in minutes,<br />- \( T \) is the time it takes for one division (20 minutes).<br /><br />First, convert 5 hours into minutes:<br /><br />\[ 5 \text{ hours} \times 60 \text{ minutes/hour} = 300 \text{ minutes} \]<br /><br />Now, plug in the values into the formula:<br /><br />\[ N = 1 \times 2^{(300/20)} \]<br /><br />Simplify the exponent:<br /><br />\[ N = 2^{15} \]<br /><br />Calculate \( 2^{15} \):<br /><br />\[ 2^{15} = 32768 \]<br /><br />So, the number of E. coli bacteria after 5 hours is 32,768.<br /><br />Therefore, the correct answer is:<br /><br />b. \( 3.2 \times 10^4 \)