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**A.**
| t    | 0   | 1   | 2   | 3   | 4   | 5   | 6      | 7   |
| ---- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| p(t) |  1000   |1100|  1210|  1331   |  1464   |1610|1771 |1948
|     |


**B.** A possible Formula is: P(t)= 1000(1.1)^t

**C.** What will the population be after 100 years under this model?     
 Population after 100 years: P(t)= 1000(1.1)^100= 13,780,612 million people

**D.** P'(1)=1210-1000/2
P'(2)=1331-1100/2
P'(3)=1464-1210/2
P'(4)=1610-1331/2
P'(5)=1771-1464/2
P'(6)=1948-1610/2
| t     | 1   | 2   | 3   | 4   |   5  | 6  |
| ----- | --- | --- | --- | --- | --- | --- |
| P'(t) | 105 | 115 | 127 | 139 |  153   | 169|
If P(5)= 1610 at the end of the 6th year,  the predicted population is 1610+153=1763 people.
P'(5) indicates the rate at which the population is increasing at the end of the 5th year. 

**E.**
P''(t)=P'(t+1)-P'(t-1)/2
  
  P''(3)=P'(4)-p'(2)/2
  
  =139-115/2=12
  
  This indicates rate of increase of populaiton after 3rd year. 
  
**F.** X



