Question

PLEASE HELP!!!!!! 100 POINTS!!!!!!!!

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

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Answer the following problem:

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.

1. What is your growth rate between 2 and 10? = 3

2. Start with 1 single bacterium and make a table showing from 0-6 hours.

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

3. Why is this table representing exponential growth? (Think about the definition and what happens from term to term as x increases by 1 what is happening to your y values?

The number of bacterium is 3 and it shows the exponential growth because every hour it is multiplied by 3, and it will always be multiplied by 3.

4. Using this example show why any nonzero number raised to a power of zero is equal to one. (Use a pattern starting at n3 =?, n2=?, n1=?, and following this pattern n0 will always equal one.)

The reason that any number to the zero power is one is that any number to the zero is just the product of no numbers which means that is the multicative identity of 1.

5. Write the rule for this table. Now find how many bacteria are present after 24 hours have passed.

Rule: y=1+3^x (to the power of X) ( use the correct form y=abx)

How many bacteria are present after 24 hours? Solve using the equation you wrote above.

282,429,536,481

Y=1+3^24

6. Make a new table that start with 100 bacteria instead of 1 and apply the same growth factor. What is the new rule? Describe the change in your table you observe.

New Rule: y=100+3^x (to the power of X)

New Table:

Hour 0 100 bacterium

Hour 1 103 bacterium

Hour 2 309 bacterium

Hour 3 927 bacterium

Hour 4 2781 bacterium

Hour 5 8343 bacterium

Hour 6 25,029 bacterium

Bonus: Include graphs for both of your equations.

Explanation:

For Conexus users

Answer 2

Answers are below

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.