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 showingthe number of bacteria that will be present after each hour for the first sixhours. then determine how many bacteria will be present once 24 hourshave passed.
b. explain why this table represents exponential growth.
c. using this example, explain why any number raised to a power of zero isequal to one.
d. write a rule for this table.
e. suppose you started with 100 bacteria, but they still grew by the samegrowth factor. how would your rule change? explain your answer

1. read the following excerpt from franklin d. roosevelt's "fireside chat 19":

on the other side of the picture, we must learn also to know that guerilla warfare against the germans in, let us say serbia or norway, us; that a successful russian offensive against the germans us; and that british successes on land or sea in any part of the world strengthen our hands.

remember always that germany and italy, regardless of any formal declaration of war, consider themselves at war with the united states at this moment just as much as they consider themselves at war with britain or russia. and germany puts all the other republics of the americas into the same category of enemies. the people of our sister republics of this hemisphere can be honored by that fact.  

the true goal we seek is far above and beyond the ugly field of battle. when we resort to force, as now we must, we are determined that this force shall be directed toward ultimate good as well as against immediate evil. we americans are not destroyers — we are builders.

analyze the effectiveness of this excerpt. how does it function within the speech as a whole? how does the structure of the excerpt to convey the speech's purpose and key points? support your argument with evidence from the speech. (10 points)

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).