Algebra-1

Identifying Exponential Growth

To determine which function demonstrates exponential growth, we need to examine the base of the exponent in each function. The general form of an exponential function is:

where:

1.a is the initial value or coefficient,

2.b is the base of the exponent,

3.x is the exponent.

 

Criteria for Exponential Growth:

Base b > 1: The function shows exponential growth because as x increases, y increases rapidly.

 

A.

Base: 0.8 (less than 1)

Behavior: Exponential decay. As x increases, y decreases.

 

B.

Base: 1.3 (greater than 1)

Behavior: Exponential growth. As x increases, y increases rapidly.

 

C.

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