Question

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.

a. 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.
b. Explain why this table represents exponential growth.
c. Using this example, explain why any nonzero number raised to a power of zero is equal to one.
d. Write a rule for this table.
e. Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.

Answer 1

bh

Explanation:

Answer 2

Answers are below

Step-by-step explanation:

Hour 0 1 bacterium

Hour 1 3 bacterium

Hour 2 9 bacterium

Hour 3 27 bacterium

Hour 4 81 bacterium

Hour 5 243 bacterium

Hour 6 729 bacterium

After 24 hours, the number of the bacterium will reach 282,429,536,481.

B) This table represents exponential growth because of the number of bacterium always being multiplied by 3.

C) The reason that any number to the zero power is one is that any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.

D) Y = 1 + 3 to the power of x

E) The rule would change by having all of the numbers multiplied by 100 since there is 100 bacterium at Hour 0.