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Chapter 3: Problem 69

One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population.

Short Answer

Expert verified
Exponential growth models fail to account for limiting factors that restrain population growth. These include density-dependent factors (like competition, predation, and disease) and density-independent factors (like natural disasters, temperature extremes, and human activities). These limitations result in most populations experiencing logistic growth, where growth slows and eventually stops as carrying capacity is reached.

Step by step solution

01

Understand Exponential Growth Models

Exponential growth models describe situations where growth rate is proportional to the size of the population. In other words, as population size increases, the rate at which it grows also increases. This generates a J-curved graph, characteristic of unrestrained population growth.
02

Identify Factors that Limit Population Size

There are several factors that can limit the size of a population. These are often categorized into two types: Density-dependent and Density-independent factors. Density-dependent factors include competition for resources (like food, water, and space), predation, disease, and waste accumulation. Density-independent factors include natural disasters (like floods, fires, and storms), temperature extremes, and human activities.
03

Understand the Limitations of Exponential Growth Models

Exponential growth models assume that resources are unlimited and that there are no restrictions to growth. However, in reality, population growth is often slowed and eventually stopped by various limiting factors. As a result, actual population growth follows more of an S-curved graph (also known as logistic growth). This graph represents initial exponential growth that slows down and eventually ceases as carrying capacity (maximum population size that the environment can support) is reached.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that exponential functions and logarithmic functions exhibit inverse, or opposite, behavior in many ways. For example, a vertical translation shifts an exponential function's horizontal asymptote and a horizontal translation shifts a logarithmic function's vertical asymptote.

The exponential models describe the population of the indicated country, \(A,\) in millions, \(t\) years after \(2010 .\) Use these models. $$\begin{aligned}&\text { India } \quad A=1173.1 e^{0.008 t}\\\&\text {lnaq}-A=31.5 e^{0.019}\\\ &\text { Japan } \quad A=127.3 e^{-0.006 t}\\\&\text { Russia } \quad A=141.9 e^{-0.005 t}\end{aligned}$$ When will India's population be 1491 million?

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