Answer :
Let's break down the problem step by step to determine the correct function that can represent the thickness of the ice shelf in meters \( x \) days since the discovery.
1. Initial Condition:
- When Naomi first discovered the ice shelf, its thickness was approximately \( 550 \) meters.
2. Rate of Decrease:
- The thickness of the ice shelf is decreasing, which means it's getting thinner over time.
- The ice shelf is decreasing at a constant rate of \( 0.08 \) meters per day.
3. Understanding the Decrease:
- The term "decreasing" suggests that for each day \( x \) that passes, the thickness of the ice shelf is reduced by \( 0.08 \) meters.
4. Formulating the Function:
- We need a function \( f(x) \) that represents the thickness of the ice shelf after \( x \) days.
- Initially (when \( x = 0 \)), the thickness of the ice shelf is \( 550 \) meters.
- As each day passes, the thickness reduces by \( 0.08 \) meters per day.
- Therefore, after \( x \) days, the reduction in thickness would be \( 0.08 \times x \).
5. Building the Function:
- The initial thickness minus the total reduction over \( x \) days gives us the current thickness.
- This is written mathematically as:
[tex]\[ f(x) = 550 - 0.08 \times x \][/tex]
6. Checking the Options:
- Option A: \( f(x) = 550 - 0.08 x \)
- This matches our formulation directly.
- Option B: \( f(x) = -0.08(x + 550) \)
- This does not represent the correct linear relationship for decreasing thickness.
- Option C: \( f(x) = 550 + 0.08 x \)
- This incorrectly suggests the thickness increases over time.
- Option D: \( f(x) = 0.08(x + 550) \)
- This does not represent the correct linear relationship for decreasing thickness.
7. Conclusion:
- The correct function to model the thickness of the ice shelf in meters \( x \) days since its discovery is:
[tex]\[ \boxed{f(x) = 550 - 0.08x} \][/tex]
Thus, the correct option is:
A. [tex]\( f(x) = 550 - 0.08 x \)[/tex]
1. Initial Condition:
- When Naomi first discovered the ice shelf, its thickness was approximately \( 550 \) meters.
2. Rate of Decrease:
- The thickness of the ice shelf is decreasing, which means it's getting thinner over time.
- The ice shelf is decreasing at a constant rate of \( 0.08 \) meters per day.
3. Understanding the Decrease:
- The term "decreasing" suggests that for each day \( x \) that passes, the thickness of the ice shelf is reduced by \( 0.08 \) meters.
4. Formulating the Function:
- We need a function \( f(x) \) that represents the thickness of the ice shelf after \( x \) days.
- Initially (when \( x = 0 \)), the thickness of the ice shelf is \( 550 \) meters.
- As each day passes, the thickness reduces by \( 0.08 \) meters per day.
- Therefore, after \( x \) days, the reduction in thickness would be \( 0.08 \times x \).
5. Building the Function:
- The initial thickness minus the total reduction over \( x \) days gives us the current thickness.
- This is written mathematically as:
[tex]\[ f(x) = 550 - 0.08 \times x \][/tex]
6. Checking the Options:
- Option A: \( f(x) = 550 - 0.08 x \)
- This matches our formulation directly.
- Option B: \( f(x) = -0.08(x + 550) \)
- This does not represent the correct linear relationship for decreasing thickness.
- Option C: \( f(x) = 550 + 0.08 x \)
- This incorrectly suggests the thickness increases over time.
- Option D: \( f(x) = 0.08(x + 550) \)
- This does not represent the correct linear relationship for decreasing thickness.
7. Conclusion:
- The correct function to model the thickness of the ice shelf in meters \( x \) days since its discovery is:
[tex]\[ \boxed{f(x) = 550 - 0.08x} \][/tex]
Thus, the correct option is:
A. [tex]\( f(x) = 550 - 0.08 x \)[/tex]
