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
2
3
4
5
6
Question 3
Explain why this table represents exponential growth.(2 points)
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Question 4
Using this example, explain why any nonzero number raised to a power of zero is equal to one.(1 point)
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Question 5
Write a rule (equation) for this table.(1 point)
Question 6
Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.(2 points)
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Question 1
My bacteria will increase 8 times every hour.
Question 2
Using an hourly growth rate of 8:
hours population
0 1
1 8
2 64
3 512
4 4,096
5 32,768
6 262,144
After 24 hours, the population would be 1,073,741,824.
Question 3
This table represents exponential growth because the population of bacteria is increasing at a constant rate by a factor of 8 every hour. Each new population is calculated by multiplying the previous population by 8.
Question 4
Any non-zero number raised to the power of zero is equal to one because it represents the concept of an empty product. When multiplying a number by itself zero times, the result is one.
Question 5
The rule (equation) for this table would be:
population = initial population * growth rate^hours
Question 6
If we started with 100 bacteria, but they still grew by a growth factor of 8, the rule would change to:
population = initial population * growth rate^hours + initial population
This is because we need to account for the initial population of 100 before applying the growth rate.