Let’s analyze the given exponential expression [tex]\(5 e^{3x + 1} + 2\)[/tex].
An expression can generally be broken down into simpler components, called terms. When we refer to terms in the context of an algebraic expression, we are looking at parts being added or subtracted. Let's write down the expression clearly:
[tex]\[ 5 e^{3x + 1} + 2 \][/tex]
1. Identify the terms:
- The expression has two parts, one involving the constant term [tex]\(2\)[/tex] and the other involving a multiplication of constants and an exponential function [tex]\(5 e^{3x + 1}\)[/tex].
2. Term Analysis:
- The first term [tex]\(2\)[/tex] is a simple constant.
- The second term [tex]\(5 e^{3x + 1}\)[/tex] is more complex as it involves an exponential function.
So, when breaking down the expression [tex]\(5 e^{3x + 1} + 2\)[/tex]:
- We identify [tex]\(2\)[/tex] as the first term, which is a constant.
- The expression [tex]\(5 e^{3x + 1}\)[/tex] as the second term, which includes the exponential function.
Therefore, the terms in the exponential expression [tex]\( 5 e^{3x + 1} + 2 \)[/tex] are:
[tex]\[ 2 \text{ and } 5 e^{3x + 1} \][/tex]
This corresponds to the option:
[tex]\[ \text{2 and } 5 e^{3 x+1} \][/tex]
