To determine which algebraic expression represents the phrase "the product of 16 and the time after the start," let's break down the phrase step by step.
1. Understanding "the product": The term "product" in mathematics refers to the result of multiplying two numbers. Therefore, we are looking for an expression that involves multiplication.
2. Identifying the elements: The phrase specifies "16" and "the time after the start" (which we can represent as a variable, say [tex]\( t \)[/tex]).
3. Formulating the expression: The phrase "the product of 16 and the time" means we need to multiply 16 by [tex]\( t \)[/tex], which can be expressed algebraically as:
[tex]\[
16 \cdot t \quad \text{or simply} \quad 16t
\][/tex]
Next, let's evaluate the given options:
- Option A: [tex]\( 16 + t \)[/tex]
This represents the sum of 16 and the time [tex]\( t \)[/tex], which is not a product.
- Option B: [tex]\( 16 - t \)[/tex]
This represents the difference between 16 and the time [tex]\( t \)[/tex], which is also not a product.
- Option C: [tex]\( \frac{16}{t} \)[/tex]
This represents the division of 16 by the time [tex]\( t \)[/tex], which again is not a product.
Given the phrase "the product of 16 and the time after the start," none of the provided options (A, B, or C) accurately represent it.
Therefore, the correct conclusion is: None of the given options accurately represents "the product of 16 and the time after the start."
