Sooty Tern In 1979, there were 12 million sooty terns (a...

Sooty Tern In $1979,$ there were 12 million sooty terns (a bird) in the world. Assume that the percentage of terns that survive from year to year has stayed constant at $83 \%$ and that approximately 2.04 million terns hatch each year. (Source: Bryan Nelson, Seabirds: Their Biology and Ecology, New York: Hamlyn Publishing Group, 1979 ) a. How many of the terns that were alive in 1979 are still alive? b. Write a function for the number of terns that hatched $t$ years after 1979 and are still alive. c. Estimate the present population of sooty terns.

Sooty Tern In $1979,$ there were 12 million sooty terns (a bird) in the world. Assume that the percentage of terns that survive from year to year has stayed constant at $83 \%$ and that approximately 2.04 million terns hatch each year. (Source: Bryan Nelson, Seabirds: Their Biology and Ecology, New York: Hamlyn Publishing Group, 1979 )
a. How many of the terns that were alive in 1979 are still alive?
b. Write a function for the number of terns that hatched $t$ years after 1979 and are still alive.
c. Estimate the present population of sooty terns.

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Key Concepts

Exponential Decay

This concept involves a quantity decreasing over time at a rate proportional to its current value. In population studies, when a fixed percentage of individuals survive from one period to the next, the decline in the number of survivors can be modeled with an exponential decay function.

Population Modeling

Population modeling uses mathematical tools to simulate and predict changes in a population over time. It incorporates processes such as reproduction (hatching) and survival, which are essential in calculating future population sizes based on current dynamics.

Recurrence Relations and Geometric Series

In population dynamics, recurrence relations help describe how a population evolves by relating the current population size to its previous size after accounting for survival and new individuals added. When each new cohort experiences constant proportional survival, the sequence of surviving individuals forms a geometric series, enabling the use of summation techniques to estimate the overall population over time.

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