Question

A. Suppose you start with one single bacterium. Make a table of values showing

Answer 1

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)