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
