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Chapter 3: Problem 62

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

Short Answer

Expert verified
Exponential growth is indicated when the base of the exponential model, 'b', is greater than 1 (b > 1). Conversely, exponential decay is signified when 'b' is between 0 and 1 (0 < b < 1).

Step by step solution

01

Understand the exponential model

An exponential model is represented by the equation \(y = ab^x\). Here, 'y' is the quantity, 'a' is the initial quantity, 'b' is the base, and 'x' is the variable usually representing time.
02

Identify the base factor (b) in the model

In an exponential model, the base factor 'b' determines if the model is describing growth or decay.
03

Distinguish between growth and decay

If the base 'b' is greater than 1 (b > 1), then the model indicates exponential growth as the quantity increases over time. On the other hand, if the base 'b' lies between 0 and 1 (0 < b < 1), then the model indicates exponential decay as the quantity decreases over time.

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