Which function does NOT represent exponential growth?

[tex]y=3(2)^x[/tex]

[tex]y=0.2(3)^x[/tex]

[tex]y=0.3(2)^x[/tex]

[tex]y=3(0.2)^x[/tex]

Identify the base b in each function of the form y = a ( b ) x .
Determine if 1"> b > 1 (exponential growth) or 0 < b < 1 (exponential decay).
The function y = 3 ( 0.2 ) x has a base of 0.2, which is between 0 and 1, indicating exponential decay.
Therefore, the function that does NOT represent exponential growth is y = 3 ( 0.2 ) x ​ .

Explanation

Understanding Exponential Growth We are given four functions and need to identify the one that does not represent exponential growth. The general form of an exponential function is y = a ( b ) x , where a is the initial value and b is the growth/decay factor. For exponential growth, the base b must be greater than 1. If 0 < b < 1 , the function represents exponential decay.

Identifying the Base Let's examine each function:

y = 3 ( 2 ) x : The base is 2, which is greater than 1. This represents exponential growth.

y = 0.2 ( 3 ) x : The base is 3, which is greater than 1. This represents exponential growth.

y = 0.3 ( 2 ) x : The base is 2, which is greater than 1. This represents exponential growth.

y = 3 ( 0.2 ) x : The base is 0.2, which is between 0 and 1. This represents exponential decay.

Conclusion The function that does not represent exponential growth is y = 3 ( 0.2 ) x because its base, 0.2, is between 0 and 1, indicating exponential decay.


Examples
Exponential growth and decay are useful for modeling various real-world phenomena. For example, population growth, compound interest, and the decay of radioactive substances can all be modeled using exponential functions. Understanding exponential functions helps in making predictions and informed decisions in fields like finance, biology, and environmental science.

Answered by GinnyAnswer | 2025-07-08

The function that does not represent exponential growth is y = 3 ( 0.2 ) x because its base, 0.2, is between 0 and 1, indicating exponential decay. The other functions have bases greater than 1, which indicates exponential growth.
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Answered by Anonymous | 2025-08-22