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Chapter 4: Problem 126

Logarithmic models are well suited to phenomena in which growth is initially rapid but then begins to level off. Describe something that is changing over time that can be modeled using a logarithmic function.

Short Answer

Expert verified
The growth of a social media app's user base over time can be an example of a phenomenon that can be modeled using a logarithmic function. This is because it often shows rapid growth initially, but the rate of growth levels off as the potential user base gets saturated.

Step by step solution

01

Understanding Logarithmic Functions

Logarithmic functions are mathematical concepts that depict a rapid increase at the beginning of an occurrence, event or system, after which the rate of increase begins to level off over time.
02

Identifying an example

One typical example of a system that can be modeled using a logarithmic function is the growth of a social media app's user base. When such an app is launched, it typically experiences rapid growth as more and more people start using it. But after a certain point, the growth begins to flatten out because there's a limited number of potential users.
03

Detailing the example

In the early stages, each new feature or marketing campaign can cause a large increase in the number of users. However, over time, as the potential user base gets saturated, the growth levels off and eventually reaches a plateau. This changing growth rate can be well modeled by a logarithmic function.

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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.

Find the domain of each logarithmic function. $$ f(x)=\log _{5}(x+4) $$

Write each equation in its equivalent exponential form. Then solve for \(x .\) $$ \log _{3}(x-1)=2 $$

Graph \(f\) and \(g\) in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of \(f\). $$ f(x)=\ln x, g(x)=\ln (x+3) $$

Will help you prepare for the material covered in the next section. In each exercise, evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: \(\log _{2} 16\) b. Evaluate: \(\log _{2} 32-\log _{2} 2\) c. What can you conclude about $$\log _{2} 16, \text { or } \log _{2}\left(\frac{32}{2}\right) ?$$
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