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
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]
Then determine how many bacteria will be present once 24 hours have passed.
Use the formula y=abx to find how many bacteria will be present after 24 hours.
y=1[growth factor you chose earlier]24
Answer:
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=abx to create the new equation
Answer:
Assuming the growth factor chosen was 8, the table of values for the first six hours would be:
Hours
Amount of Bacteria
0
1
1
8
2
64
3
512
4
4,096
5
32,768
6
262,144
To find the number of bacteria present after 24 hours using the formula y=ab^x, we substitute the values:
y = 1 * 8^24
y = 1 * 8,388,608
y = 8,388,608
Therefore, after 24 hours, there would be 8,388,608 bacteria present.
If we start with 100 bacteria but they still grow by the same growth factor, the rule would change as the initial amount of bacteria is different. The new equation would be:
y = 100 * 8^x
This equation accounts for starting with 100 bacteria and still growing by a growth factor of 8.