# Growth and Decay - Arithmetic Growth And Decay, Geometric Growth And Decay

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rate population example sequences

Growth and decay refers to a class of problems in **mathematics** that can be modeled or explained using increasing or decreasing sequences (also called series). A sequence is a series of numbers, or terms, in which each successive **term** is related to the one before it by precisely the same formula. There are many practical applications of sequences. One example is predicting the growth of human populations. Population growth or decline has an impact on numerous economic and environmental issues. When the population grows, so does the **rate** at which waste is produced, which in turn affects growth rate of land fill sites, nuclear waste dumps, and other sources of **pollution**. Various other growth rates also affect our lives. For instance the growth rates of our investments and savings accounts, affect our economic well-being. Understanding the mathematics of growth is very important. For example, predicting the rate at which renewable resources, including the **forests**, marine life, and **wildlife**, naturally replenish themselves, helps prevent excessive harvesting that can lead to population declines and even **extinction**.

## Additional Topics

Arithmetic growth is modeled by an arithmetic sequence. In an arithmetic sequence each successive term is obtained by adding a fixed quantity to the previous term. For example, an investment that earns simple interest (not compounded) increases by a fixed percentage of the principal (original amount invested) in each period that interest is paid. A one-time investment of $1,000, in an account that…

This same compounding model can be applied to population growth. However, unlike the growth of an investment, population growth is limited by the availability of food, water, shelter, and the prevalence of disease. Thus, population models usually include a variable growth rate, rather than a fixed growth rate, that can take on negative as well as positive values. When the growth rate is negative, …

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