To determine whether the function [tex]\( g(x) = 4 \cdot 5^x \)[/tex] represents exponential growth or decay, we focus on the base of the exponential term, which is the number raised to the power of [tex]\( x \)[/tex].
1. Identifying the base: In the function [tex]\( g(x) = 4 \cdot 5^x \)[/tex], the term [tex]\( 5^x \)[/tex] indicates that the base of the exponent is 5.
2. Understanding exponential growth and decay:
- Exponential growth occurs when the base of the exponent is greater than 1.
- Exponential decay occurs when the base of the exponent is between 0 and 1.
3. Analyzing the base: The base in the given function is 5. Since 5 is clearly greater than 1, it indicates that the function represents exponential growth.
Therefore, the correct statement is:
- The function represents exponential growth because the base equals 5.
