Answer to Question 3

3.  

a.  Complete the chart:

Time intervals
30 minutes		 1
.5 hr		 2
1 hr		 3
1.5 hr		 4
2 hr		 5
2.5 hr		 6
3 hr		 7
3.5 hr		 8
4 hr		 9
4.5 hr		 10
5 hr
Bacteria present 2000 4000 8000 16000 32000 64000 128000 256000 512000 1024000
Pattern: 1000*21 1000*22 1000*23 1000*24 1000*25 1000*26 1000*27 1000*28 1000*29 1000*210

b.  Function:                    From pattern:   

 

c.  Graph:  horizontal axis = 30 min. time intervals
                    vertical axis = number of bacteria

d.  Find the number of bacteria present after 45 minutes. 
From looking at the data table:  45 minutes is half way between 30 minutes and one hour.  If this process were "linear" we could make an estimate of the bacteria to be half way between 2000 and 4000 which would be 3000 bacteria.  However, exponential growth is not linear.  If you examine the graph, the number of bacteria at 45 minutes equals  2828.4271 bacteria.

 

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