West African Elephants There were once more than 1 mil- lion elephants in West Africa. Now, howe

step 1 Hello. So part A, we have the initial population of elephants is 19 ,000. And of these, we have

West African Elephants There were once more than 1 mil- lion...

West African Elephants There were once more than $1 \mathrm{mil}-$ lion elephants in West Africa. Now, however, the elephant population has dwindled to $19,000 .$ Each year, $17.8 \%$ of West Africa elephants die or are killed by hunters. At the same time, elephant births are decreasing by $13 \%$ per year. (Source: Douglas Chadwick, The Fate of the Elephant, San Francisco: Sierra Club Books, 1992 ) a. How many of the current population of 19,000 elephants will still be alive 30 years from now? b. Considering that 47 elephants were born in the wild this year, write a model for the number of elephants that will be born $t$ years from now and will still be alive 30 years from now. c. Calculate the elephant population of West Africa 30 years from now.

West African Elephants There were once more than $1 \mathrm{mil}-$ lion elephants in West Africa. Now, however, the elephant population has dwindled to $19,000 .$ Each year, $17.8 \%$ of West Africa elephants die or are killed by hunters. At the same time, elephant births are decreasing by $13 \%$ per year. (Source: Douglas Chadwick, The Fate of the Elephant, San Francisco: Sierra Club Books, 1992 )
a. How many of the current population of 19,000 elephants will still be alive 30 years from now?
b. Considering that 47 elephants were born in the wild this year, write a model for the number of elephants that will be born $t$ years from now and will still be alive 30 years from now.
c. Calculate the elephant population of West Africa 30 years from now.

Key Concepts

Exponential Decay

Exponential decay describes how a quantity decreases by a constant percentage over time. In population dynamics, it is used to model how a population reduces due to consistent mortality or other loss factors, which is key to predicting the survivors after a given number of years.

Population Modeling

Population modeling uses mathematical equations to forecast changes in the number of individuals in a population over time. This subject incorporates factors like death rates and birth rates to create predictive models, which are crucial for understanding long-term trends in species populations.

Survival Probability

Survival probability is the likelihood that an individual will remain alive over a specific period, given recurring hazards or mortality rates. This concept is applied repeatedly over time intervals in order to estimate how many individuals will survive into the future.

Birth Rate Modeling

Birth rate modeling involves representing the process of new individuals being added to the population, often by integrating the birth rate with survival probabilities. This is essential when predicting not only how many births will occur but also how many of these new individuals will survive over time.

Multiplicative Factors in Compounded Processes

Multiplicative factors come into play when a constant rate of survival or loss is applied repeatedly over several periods. This concept, similar to compound interest in finance, is fundamental in calculating the accumulated effect on a population over many years.

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