Mitosis is a process of cell reproduction in which one cell divides into two identical cells. A bacterium called E. coli often causes serious food poisoning. It can reproduce itself in 15 minutes.
a) Starting with one bacterium, make a table with time in 1/4 -h blocks and the corresponding number of E. coli
b) Make a scatter plot from the table of data.
c) What conclusions can you make from examining the table and scatter plot?
d) About how long will it take before there are 10,000 bacteria?
PLEASE ANSWER, I DON'T UNDERSTAND HOW TO CALCULATE THE LAST PART (D). I DID EVERYTHING ELSE.
AT 195 MINS. = 8192
AT 210 MINS. = 16,384
HOW DO I CALCULATE THE APPROX. TIME WHEN BACTERIA IS MULTIPLIED TO 10,000.
THANK YOU!!!
after t minutes, there are 2^(t/15) bacteria. So, find t when
2^(t/15) = 10000
t/15 log2 = log10000
t = 15 * (log10000/log2)
Thanks for answering my question! By the way what is that sort of question called? Could you write the answer if you know it on my question page where you previously answered!
it's a problem in exponential growth
similar ones in exponential decay are things like radiocarbon dating, where the amount of carbon-14 diminishes each year by a certain small percentage.
Mitosis is a process of cell reproduction in which one cell divides into two identical cells. A bacterium called E. coli often causes serious food poisoning. It can reproduce itself in 15 minutes. a) Starting with one bacterium, make a table with time in 1/4 -h blocks and the corresponding number of E. coli b) Make a scatter plot from the table of data. c) What conclusions can you make from examining the table and scatter plot? d) About how long will it take before there are 10,000 bacteria? answer
To calculate the approximate time it takes for the number of bacteria to reach 10,000, you can use the data you already have and extrapolate from it. Follow these steps:
1. Look at the time intervals in your table and the corresponding number of E. coli at those intervals. By examining the data, you can see that the number of bacteria doubles in each time interval.
2. Calculate the growth factor by dividing the number of bacteria at one time interval by the number at the previous interval. For example, from 195 minutes to 210 minutes, the growth factor is 16,384 / 8,192 = 2.
3. Determine how many doubling intervals it takes for the number of bacteria to reach 10,000. You can use logarithms to solve this. Since the growth factor is 2, you need to find the logarithm base 2 of 10,000.
4. Use the logarithm function in your calculator to find the logarithm base 2 of 10,000. This will give you the number of doubling intervals required.
5. Multiply the number of doubling intervals by the time interval to estimate the time it takes for the number of bacteria to reach 10,000. In this case, the time intervals are in 1/4-hour blocks, so you'll need to convert the time to minutes or hours before multiplying.
Here's a step-by-step example calculation:
1. Growth factor: 2 (as observed from the data)
2. Number of doubling intervals: log2(10,000) ≈ 13.288
3. Time in minutes for 13.288 doubling intervals: 13.288 x (15 minutes) = 199.32 minutes
Therefore, it will take approximately 199 minutes and 19 seconds for the number of bacteria to reach 10,000.
Keep in mind that this is an estimation and assumes exponential growth without any limiting factors. In reality, factors like resource availability, competition, and other conditions may affect the growth rate.