Limits -- Answers

The example in the module on pack-hunters
```
R(p) = 0.5 + 0.003 p - 0.000002166667 p (p - 500)
p(n + 1) = R(p(n)) * p(n)
```
The first graph appears to show a sequence with a limit of zero. The other two graphs show sequences that are not going to a limit.

Next we look at the "check your understanding questions" from the Pack Hunters module.

        1  200.00        6    0.00
        2  120.00        7    0.00
        3   43.20        8    0.00
        4    5.60        9    0.00
        5    0.09       10    0.00

  Lim   p(n) = 0
n --> oo

        1  400.00        6  999.92
        2  480.00        7 1000.00
        3  691.20        8 1000.00
        4  904.64        9 1000.00
        5  990.91       10 1000.00

  Lim   p(n) = 1000
n --> oo

        1  600.00        6 1000.00
        2  840.00        7 1000.00
        3  974.40        8 1000.00
        4  999.34        9 1000.00
        5 1000.00       10 1000.00

  Lim   p(n) = 1000
n --> oo

        1  800.00        6 1000.00
        2  960.00        7 1000.00
        3  998.40        8 1000.00
        4 1000.00        9 1000.00
        5 1000.00       10 1000.00

  Lim   p(n) = 1000
n --> oo

        1  200.00        6    0.20
        2  160.00        7    0.00
        3  102.40        8    0.00
        4   41.94        9    0.00
        5    7.04       10    0.00

  Lim   p(n) = 0
n --> oo

        1  400.00        6 1515.39       11 1499.51       16 1500.02
        2  640.00        7 1492.07       12 1500.25       17 1499.99
        3 1190.40        8 1503.90       13 1499.88       18 1500.00
        4 1558.95        9 1498.03       14 1500.06       19 1500.00
        5 1467.05       10 1500.98       15 1499.97       20 1500.00

  Lim   p(n) = 1500
n --> oo

        1  600.00        6 1493.28       11 1500.21       16 1499.99
        2 1140.00        7 1503.32       12 1499.90       17 1500.00
        3 1550.40        8 1498.33       13 1500.05       18 1500.00
        4 1472.26        9 1500.83       14 1499.97       19 1500.00
        5 1513.10       10 1499.58       15 1500.01       20 1500.00

  Lim   p(n) = 1500
n --> oo

        1  800.00        6 1493.28       11 1500.21       16 1499.99
        2 1360.00        7 1503.32       12 1499.90       17 1500.00
        3 1550.40        8 1498.33       13 1500.05       18 1500.00
        4 1472.26        9 1500.83       14 1499.97       19 1500.00
        5 1513.10       10 1499.58       15 1500.01       20 1500.00

  Lim   p(n) = 1500
n --> oo

Copyright c 1995 by PWS Publishing Company, a division of International Thomson Publishing Inc. Comments to Frank Wattenberg, Department of Mathematics, Carroll College, Helena, MT 59625.