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.