Exponential Growth and Stuff

[DripKracken]

I have a math portfolio and im not really sure how to do the whole thing. The black text and table are my answers. I cant figure out how to write a rule.
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.

• 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.

• Bacteria	Time
  1	1
  4	7
  16	13
  64	19
  256	25

  • Explain why this table represents exponential growth.
  • This table represents exponential growth because the amount of bacteria quadruples every six hours.
  • Using this example, explain why any nonzero number raised to a power of zero is equal to one.
  • Nonzero numbers raised to zero equal one because going to the power of 0 is like the product of no numbers.
  • Write a rule for this table.
  • Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.

 

[lev888]

I have a math portfolio and im not really sure how to do the whole thing. The black text and table are my answers. I cant figure out how to write a rule.
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.

• 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.

• Bacteria	Time
  1	1
  4	7
  16	13
  64	19
  256	25

  • Explain why this table represents exponential growth.
  • This table represents exponential growth because the amount of bacteria quadruples every six hours.
  • Using this example, explain why any nonzero number raised to a power of zero is equal to one.
  • Nonzero numbers raised to zero equal one because going to the power of 0 is like the product of no numbers.
  • Write a rule for this table.
  • Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.

Time 1 means we are at 1 hour mark. Why is the number of bacteria still 1 if it's supposed to quadruple? Where is the data for "each hour for the first six hours"?
Exponential growth should involve an exponent somewhere, no?

 

[DripKracken]

so what about this?

Bacteria	Time (in hours)
4	1
16	2
64	3
256	4
1024	5
4096	6

 

[lev888]

so what about this?

Bacteria	Time
4	1
16	2
64	3
256	4
1024	5
4096	6

See the pattern in left column? What's the rule?

 

[DripKracken]

it multiplies by 4 every hour

 

[JeffM]

I have a math portfolio and im not really sure how to do the whole thing. The black text and table are my answers. I cant figure out how to write a rule.
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.

• 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.

• Bacteria	Time
  1	1
  4	7
  16	13
  64	19
  256	25

  • Explain why this table represents exponential growth.
  • This table represents exponential growth because the amount of bacteria quadruples every six hours.
  • Using this example, explain why any nonzero number raised to a power of zero is equal to one.
  • Nonzero numbers raised to zero equal one because going to the power of 0 is like the product of no numbers.
  • Write a rule for this table.
  • Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.

First, you only give the number of bacteria at the end of the first FOUR hours. The 1 bacterium is present at the start of the first hour or, if you prefer, at the end of the zeroth hour. The start of hour number x is the end of hour number x - 1, no?

ok you fixed that. Great.

Second, what the world are the numbers under time supposed to represent?

You basically fixed that, but you actually made things a bit more difficult by dropping the initial state of 1 bacterium.

Third, what does quadrupling have to do with exponential growth?

Fourth, the question about non-zero numbers raised to the power of zero is actually quite tricky. But your answer makes no sense at all. If I have no rooms with no cats in them, why should I have a cat?

To give you a hint

At the end of the second hour, you have 16 = 4 * 4 bacteria

At the end of the third hour, you have 64 = 4 * 16 = 4 * 4 * 4 bacteria

At the end of the fourth hour, you have 256 = 4 * 64 = 4 * 4 * 16 = 4 * 4 * 4 * 4.

Hmm, how does that relate to exponents?

 

[Steven G]

• Nonzero numbers raised to zero equal one because going to the power of 0 is like the product of no numbers.

So the product of no numbers (what ever that means) is 1.

In the blank space below you see no numbers, correct? So the product of those numbers is 1? I am sure that you do not believe that. Be more careful with what you say.