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Help Plz!! Bacteria are the most common example of exponential growth. Research and find a
bacterium that grows each hour exponentially and determine how much it grows
per 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. 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.

Respuesta :

Gladistshiala267

a) table of values, star = t = 0, and B = 1


time (t)    number of bacteria (B)


0              1


1              2


2              4


3              8


4              16


5               32


6               64


=> B = 2^t


t = 24 hours => B = 2^24 =  16,777,216        


b) The data shows that every hour the number of bacteria is duplicated, which resulted in the model B = 2^t which is an exponential function, explainging the exponential growth.


c) t = 0 => starting moment, at that moment the number of bacteria is alway 1, this a simple way of seing intuitively that no matter the base (which in this case was 2) the number of bacteria is the starting number (1)


d) I already wrote the rule: B = 2^t


e) if you start with 100 bacteria the model will be


After 1 hour you will have 100*2. after two hours 100*2*2, after three hours 100*2*2*2, after four hours 100*2*2*2*2, then after t hours B = 100 (2)^t


As you see the startiing value becomes a coefficient of the exponential function.  


B = 100 (2^t)

 

hope this helps

The population of bacteria is exponential growth.

In 24 hours, the population of the bacteria is 16,777,216.The function B = 2^t which is an exponential function.At t = 0, the population of the bacteria is 1.The exponent rule is applied.The population of the bacteria gets 100 times.

What is an exponent?

An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Given

Bacteria are the most common example of exponential growth.

a. Suppose you start with one single bacterium.

Let the function [tex]\rm B= 2^t[/tex]

Then the table will be.

[tex]\begin{aligned} & \rm Time (t) \ \ \ \ &\rm Number \ of \ Bacteria (B)\\&0 &1 \\ &1 &2 \\ &2 &4 \\ &3 &8 \\ &4 & 16 \\ & 5 & 32\\ & 6 & 64\end{aligned}[/tex]

In 24 hours, the population of the bacteria will be

[tex]\rm B = 2^t\\\\B = 2^{24}\\\\B =16777216[/tex]

In 24 hours, the population of the bacteria is 16,777,216.

b)  The data shows that every hour the number of bacteria is doubled, which resulted in the function B = 2^t which is an exponential function, explaining the exponential growth.

c)  At t = 0, the population of the bacteria is 1.

d)  The exponent rule is applied. every hour the number of bacteria is doubled.

e)  Suppose you started with 100 bacteria, but they still grew by the same growth factor. Then the population of the bacteria gets 100 times. That is given by

[tex]\rm B = 100 * 2^t[/tex]

More about the exponent link is given below.

https://brainly.com/question/219134

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