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.

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)