Task 1 - Bacteria Population Growth
Bacteria are the most common example of exponential growth. In this task, you will choose an hourly growth rate between 2 and 10 for some bacteria.
You will start with 1 bacteria and then calculate the total population after certain amounts of time.
Question 1
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
(1 point)
My bacteria will increase times every hour.
Question 2
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. Then determine how many bacteria will be present once 24 hours have passed.(6 points)
hours population
0 1
1 88
2 6464
3 512512
4 40964096
5 32 comma 76832,768
6 262 comma 144262,144
Question 3
Explain why this table represents exponential growth.(2 points)
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This table represents exponential growth because as the hours increase, the population also increases at a rapid rate. The population values in the table are increasing significantly with each hour, indicating exponential growth.
33 / 10000 Word Limit33 words written of 10000 allowed
Question 4
As we can see, the value of 2 raised to increasing powers gets larger and larger. However, when we raise 2 to the power of 0, it becomes 1.
This pattern can be generalized to any nonzero number. When a nonzero number is raised to the power of 0, it essentially means that we are not multiplying the number by itself at all. We are multiplying it zero times.
BoldItalicUnderlineBullet listNumbered list
As we can see, the value of 2 raised to increasing powers gets larger and larger. However, when we raise 2 to the power of 0, it becomes 1.
This pattern can be generalized to any nonzero number. When a nonzero number is raised to the power of 0, it essentially means that we are not multiplying the number by itself at all. We are multiplying it zero times.
69 / 10000 Word Limit69 words written of 10000 allowed
Question 5
Write a rule (equation) for this table.(1 point)
Question 6
The rule (equation) for this table is:
population = (initial population) * (growth rate)^number of hours