Answer :
To solve this problem, let's analyze the information provided in the table and determine which statement correctly describes Katy's walk towards the bridge.
The table gives us the following data points:
[tex]\[ \begin{tabular}{|c|c|} \hline x & f(x) \\ \hline 0 & 300 \\ \hline 1 & 250 \\ \hline 2 & 200 \\ \hline 3 & 150 \\ \hline 4 & 100 \\ \hline 5 & 50 \\ \hline 6 & 0 \\ \hline \end{tabular} \][/tex]
1. Initial Distance:
[tex]\[ f(0) = 300 \][/tex]
This tells us that initially, i.e., at [tex]\( x = 0 \)[/tex] minutes, Katy was 300 meters away from the bridge.
2. Consistency of Decrease:
[tex]\[ \begin{aligned} f(1) &= 250 \quad \text{(after 1 minute)}, \\ f(2) &= 200 \quad \text{(after 2 minutes)}, \\ f(3) &= 150 \quad \text{(after 3 minutes)}, \\ f(4) &= 100 \quad \text{(after 4 minutes)}, \\ f(5) &= 50 \quad \text{(after 5 minutes)}, \\ f(6) &= 0 \quad \text{(after 6 minutes)}. \end{aligned} \][/tex]
We see that the distance decreases by 50 meters each minute consistently.
3. Reaching the Bridge:
[tex]\[ f(6) = 0 \][/tex]
This indicates that after 6 minutes, Katy reaches the bridge as her distance from it becomes 0.
With this analysis, let's evaluate the given statements:
- A. Katy was initially 300 meters from the bridge, and it took her 5 minutes to reach the bridge.
This is incorrect because it took her 6 minutes, not 5 minutes, to reach the bridge.
- B. Katy was initially 300 meters from the bridge, and it took her 6 minutes to reach the bridge.
This is correct according to our analysis.
- C. Katy was initially 250 meters from the bridge, and it took her 5 minutes to reach the bridge.
This is incorrect because she started 300 meters away, not 250 meters.
- D. Katy was initially 250 meters from the bridge, and it took her 6 minutes to reach the bridge.
This is incorrect for the same initial distance reason as in C.
Thus, the correct statement is:
[tex]\[ \boxed{B} \][/tex]
Katy was initially 300 meters from the bridge, and it took her 6 minutes to reach the bridge.
The table gives us the following data points:
[tex]\[ \begin{tabular}{|c|c|} \hline x & f(x) \\ \hline 0 & 300 \\ \hline 1 & 250 \\ \hline 2 & 200 \\ \hline 3 & 150 \\ \hline 4 & 100 \\ \hline 5 & 50 \\ \hline 6 & 0 \\ \hline \end{tabular} \][/tex]
1. Initial Distance:
[tex]\[ f(0) = 300 \][/tex]
This tells us that initially, i.e., at [tex]\( x = 0 \)[/tex] minutes, Katy was 300 meters away from the bridge.
2. Consistency of Decrease:
[tex]\[ \begin{aligned} f(1) &= 250 \quad \text{(after 1 minute)}, \\ f(2) &= 200 \quad \text{(after 2 minutes)}, \\ f(3) &= 150 \quad \text{(after 3 minutes)}, \\ f(4) &= 100 \quad \text{(after 4 minutes)}, \\ f(5) &= 50 \quad \text{(after 5 minutes)}, \\ f(6) &= 0 \quad \text{(after 6 minutes)}. \end{aligned} \][/tex]
We see that the distance decreases by 50 meters each minute consistently.
3. Reaching the Bridge:
[tex]\[ f(6) = 0 \][/tex]
This indicates that after 6 minutes, Katy reaches the bridge as her distance from it becomes 0.
With this analysis, let's evaluate the given statements:
- A. Katy was initially 300 meters from the bridge, and it took her 5 minutes to reach the bridge.
This is incorrect because it took her 6 minutes, not 5 minutes, to reach the bridge.
- B. Katy was initially 300 meters from the bridge, and it took her 6 minutes to reach the bridge.
This is correct according to our analysis.
- C. Katy was initially 250 meters from the bridge, and it took her 5 minutes to reach the bridge.
This is incorrect because she started 300 meters away, not 250 meters.
- D. Katy was initially 250 meters from the bridge, and it took her 6 minutes to reach the bridge.
This is incorrect for the same initial distance reason as in C.
Thus, the correct statement is:
[tex]\[ \boxed{B} \][/tex]
Katy was initially 300 meters from the bridge, and it took her 6 minutes to reach the bridge.
