To solve the problem, we need to evaluate the function \( h(t) = -16t^2 + 28t + 500 \) at \( t = 3.2 \).
Here is the step-by-step process:
1. Understand the problem: We are given a function \( h(t) \) that represents the height of a rock \( t \) seconds after it is propelled. We need to find out what \( h(3.2) \) represents.
2. Substitute \( t = 3.2 \) into the function:
[tex]\[
h(3.2) = -16(3.2)^2 + 28(3.2) + 500
\][/tex]
3. Evaluate the function at \( t = 3.2 \):
[tex]\[
h(3.2) = -16 \cdot 10.24 + 28 \cdot 3.2 + 500
\][/tex]
[tex]\[
h(3.2) = -163.84 + 89.6 + 500
\][/tex]
[tex]\[
h(3.2) = 425.76
\][/tex]
4. Interpret the result: The value \( h(3.2) = 425.76 \) represents the height of the rock when \( t = 3.2 \). Therefore, it indicates the height of the rock 3.2 seconds after it is propelled.
Based on this interpretation, we can conclude:
The correct answer is:
- the height of the rock 3.2 seconds after it is propelled
