• **Deer Population**

f(x) = 296.6sin(0.8x + 0.3) + 1215.7

•**Lion Population**

f(x) = 11.9sin(0.8x - 2.1) + 49.9

- -*Phase Shift*

f(x) = 296.6sin(0.8x + 0.3) + 1215.7

•

f(x) = 11.9sin(0.8x - 2.1) + 49.9

- -

Years | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 |

Deer | 1,272 | 1,523 | 1,152 | 891 | 1,284 | 1,543 | 1,128 | 917 | 1,185 |

Lions | 39 | 47 | 63 | 54 | 37 | 48 | 60 | 46 | 40 |

Number of Animals

Number of Years

(A, B)

The deer and lion populations fluctuate in ~8 year cycles.

(C)

It takes approximately 2 years from the Deer population having reached its max, for the Lion population to reach its max.

As the Lion population grows, it depletes the Deer population, which over time becomes insufficient to sustain the Lion population. Hence the Lion population begins to dwindle for lack of food supply, causing the Deer population to begin to recover.

As the Deer population recovers, the food supply to the lions becomes more plentiful, and the cycle repeats.