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Chapter 4: Problem 58

How can you tell whether an exponential model describes exponential growth or exponential decay?

Short Answer

Expert verified
An exponential model \( f(x) = ab^x \) represents exponential growth if the base \( b > 1 \), and it represents exponential decay if \( 0 < b < 1 \).

Step by step solution

01

Determine the Base

First, identify the base \( b \) of the exponential function \( f(x) = ab^x \). The base \( b \) is the number that is raised to \( x \). For example, if you have an exponential function \( f(x) = 2^x \), the base \( b \) is 2.
02

Identify the Growth/Decay

Once the base \( b \) is identified, compare it to 1. If \( b > 1 \), the function represents exponential growth. If \( 0 < b < 1 \), the function represents exponential decay. For instance, for the function \( f(x) = 2^x \), since \( b = 2 \) and \( 2 > 1 \), the function represents exponential growth.

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Most popular questions from this chapter

The figure shows the graph of \(f(x)=\ln x\). Use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. (GRAPH CANNOT COPY). $$ g(x)=2-\ln x $$

Exercises \(134-136\) will help you prepare for the material covered in the next section. Solve: \(x(x-7)=3\)

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