**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