To determine which function does NOT represent exponential growth, let's first understand what exponential growth means. An exponential growth occurs when the value of a function increases rapidly as [tex]\( x \)[/tex] increases. Mathematically, if we have a function of the form [tex]\( y = a(b)^x \)[/tex]:
- If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay, not growth.
Now let's look at each of the given functions one by one:
1. [tex]\( y = 0.3 (2)^x \)[/tex]
- In this function, [tex]\( b = 2 \)[/tex].
- Since [tex]\( b > 1 \)[/tex], this function represents exponential growth.
2. [tex]\( y = 3 (2)^x \)[/tex]
- In this function, [tex]\( b = 2 \)[/tex].
- Since [tex]\( b > 1 \)[/tex], this function represents exponential growth.
3. [tex]\( y = 0.2 (3)^x \)[/tex]
- In this function, [tex]\( b = 3 \)[/tex].
- Since [tex]\( b > 1 \)[/tex], this function represents exponential growth.
4. [tex]\( y = 3 (0.2)^x \)[/tex]
- In this function, [tex]\( b = 0.2 \)[/tex].
- Since [tex]\( 0 < b < 1 \)[/tex], this function does NOT represent exponential growth. Instead, it represents exponential decay.
Thus, the function that does NOT represent exponential growth is:
[tex]\( y = 3 (0.2)^x \)[/tex].
Therefore, the answer is function number 4.
