Task 1
Bacteria are the most common example of exponential growth. Select a number between 2 and 10 to represent the hourly growth rate of a certain bacteria. For example, selecting the number 8 would mean that the amount of bacteria will be 8 times greater after every hour. [your pick of a number between 2 and 10]
Suppose you start with one single bacterium. Make a table of values showing the number of bacteria that will be present after each hour for the first six hours using the hourly growth rate that you selected.
Hours
Amount of Bacteria
0
1
[enter amount after 1 hour]
2
[enter amount after 2 hours]
3
[enter amount after 3 hours]
4
[enter amount after 4 hours]
5
[enter amount after 5 hours]
6
[enter amount after 6 hours]
Suppose we select the number 4 as the hourly growth rate.
Hours
Amount of Bacteria
0
1
1 (starting with one bacterium)
2
4 (multiplying the previous amount by 4)
3
16 (multiplying the previous amount by 4)
4
64 (multiplying the previous amount by 4)
5
256 (multiplying the previous amount by 4)
6
1024 (multiplying the previous amount by 4)
Then determine how many bacteria will be present once 24 hours have passed.
Use the formula
y=a*b^x to find how many bacteria will be present after 24 hours.
y=1*4^24
Using the formula y = a * b^x, where a represents the initial amount of bacteria (1 in this case), b represents the growth rate (4 in this case), and x represents the number of hours (24 in this case), we can calculate the number of bacteria that will be present after 24 hours.
y = 1 * 4^24 = 1 * 16,777,216 = 16,777,216
Therefore, after 24 hours, there will be 16,777,216 bacteria present.
Then determine how many bacteria will be present once 24 hours have passed.
Use the formula
y=a*b^x to find how many bacteria will be present after 24 hours.
y=1*[growth factor you chose earlier]^24
Sure, using the formula y = a * b^x, where a represents the initial amount of bacteria (1 in this case), b represents the growth factor (4 in this case, as per the earlier selection), and x represents the number of hours (24 in this case), we can calculate the number of bacteria that will be present after 24 hours.
y = 1 * 4^24 = 1 * 268,435,456 = 268,435,456
Therefore, after 24 hours, there will be 268,435,456 bacteria present.
Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer. Use this formula
y=a*b^x to create the new equation
If we start with 100 bacteria and they still grow by the same growth factor, the initial amount (a) in the equation y = a * b^x would be different. In this case, a would be equal to 100.
Therefore, the new equation to calculate the number of bacteria after a certain number of hours would be:
y = 100 * b^x
Where b represents the growth factor chosen earlier and x represents the number of hours. This equation takes into account the initial amount of bacteria (100) and the same growth factor to determine the number of bacteria at any given time.