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ASuppose 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.

BExplain why this table represents exponential growth.
CUsing this example, explain why any nonzero number raised to a power

of zero is equal to one.

DWrite a rule for this table.
ESuppose you started with 100 bacteria, but they still grew by the same

growth factor. How would your rule change? Explain your answer.

Verified Answer :

Edufirst
Atable 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 1002. after two hours 10022, after three hours 100222, after four hours 1002222, 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)
 

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