The change in altitude (a) of a car as it drives up a hill is described by the following piecewise equation, where d is the distance in meters from the starting point. a{0.5x if d <10050 if d ≥100 Describe the change in altitude of the car as it travels from the starting point to about 200 meters away. (1 point) Responses As the car travels its altitude keeps increasing. As the car travels its altitude keeps increasing. The car’s altitude increases until it reaches an altitude of 100 meters. The car’s altitude increases until it reaches an altitude of 100 meters. As the car travels its altitude increases, but then it reaches a plateau and its altitude stays the same. As the car travels its altitude increases, but then it reaches a plateau and its altitude stays the same. The altitude change is more than 200 meters.

Answer 1

To analyze the change in altitude of the car as it travels from the starting point to about 200 meters away, we can refer to the piecewise equation provided:

• For \( d < 100 \): \( a = 0.5d \)
• For \( d \ge 100 \): \( a = 50 \)

Now, let's break this down:

1. From the starting point up to 100 meters: The altitude \( a \) is described by the equation \( a = 0.5d \). This means that for every meter the car travels, the altitude increases by 0.5 meters.

   • At \( d = 0 \): \( a = 0.5 \times 0 = 0 \) meters
   • At \( d = 100 \): \( a = 0.5 \times 100 = 50 \) meters

   Therefore, as the car travels from the starting point to 100 meters, its altitude increases steadily from 0 meters to 50 meters.

2. From 100 meters onward (up to 200 meters in this case): When \( d \ge 100 \), the altitude remains constant at 50 meters (since \( a = 50 \)).

Thus, as the car continues to travel from 100 meters to 200 meters, the altitude does not increase—it remains at 50 meters.

Given this analysis, the correct description of the change in altitude of the car as it travels from the starting point to about 200 meters away is:

"As the car travels, its altitude increases but then it reaches a plateau and its altitude stays the same."