Question

vernon is studying the population of deer in a tract of forest. he gathers the following data.

birth rate:~50 deer/year

death rate:~70 deer/year

which additional observation would support the conclusion that the deer population is not changing size from year to year, meaning that the net population change is 0?

a. about 20 deer per year immigrate to the tract of forest.

b. about 20 deer per year emigrate from the tract of forest.

c. the average life span of a member of the deer population is 20 years.

d. if a deer survives its first year of life, its average life span is 20 years.

Explanation:

To determine the net population change, we use the formula: Net Population Change = (Births - Deaths) + (Immigration - Emigration). Given Birth rate = 50 deer/year and Death rate = 70 deer/year, the difference from births and deaths is \(50 - 70=- 20\) deer/year. For the net change to be 0, the (Immigration - Emigration) term must be +20. This means Immigration - Emigration = 20. If about 20 deer per year immigrate (Immigration = 20) and Emigration = 0, then \(20 - 0 = 20\), which balances the -20 from births and deaths. Let's check the options:

• Option A: Immigration = 20. Then (Births - Deaths)+(Immigration - Emigration)= \((50 - 70)+(20 - 0)=- 20 + 20 = 0\). This works.
• Option B: Emigration = 20. Then \((50 - 70)+(0 - 20)=-20-20=-40

eq0\).

• Options C and D: Life span information does not relate to population change (birth, death, immigration, emigration), so they are irrelevant.

Answer:

A. About 20 deer per year immigrate to the tract of forest.