Deer have become increasingly apparent in a rural county. Last year it was estim

Question

Deer have become increasingly apparent in a rural county. Last year it was estimated that there were 40 breeding pairs (a deer must reach the age of 1 to breed). A pair of deer produce an average of 1 fawn per year, and 80% of these fawns grow to reach 1 year of age. 10% of adult deer die of natural causes each year. An average of 5 adult deer are killed annually in highway accidents, and 2 per year in illegal hunting. Use difference equations to estimate the population of deer. Do you think it is likely that the deer population in the county is increasing? Will the deer population eventually reach equilibrium?

Explanation / Answer

40 breeding pairs (a deer must reach the age of 1 to breed).

A pair of deer produce an average of 1 fawn per year, and 80% of these fawns grow to reach 1 year of age

An average of 5 adult deer are killed annually in highway accidents, and 2 per year in illegal hunting.

As there 40 breeding pais, where 1 fawn per year (80 % reach 1 year age)

40 * 80 % = 32 fawns.

Adult deer killed - 5 + 2 = 7.

Total dear = (40 *2 - 7) = 73

Add new fawns = 73 + 32 = 105 (End of the year)

Yes the deer population of Deer increasing as it reaches 105 by the end of the year (from previous year 73).

Yes as the year progresses in third year it will reach equilibrium & even exceeds from there.

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