Question

stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height, h(t), in meters (as it relates to sea level), of the sunglasses after t seconds, is shown in the table.
height of sunglasses over time

t	h(t)
1	5.1
2	-9.6
3	-34.1
4	-68.4
5	-112.5
6	-166.4
7	-230.1

during its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. to the nearest meter, what is the difference in elevation between stefano and the climber?

• 166 meters
• 176 meters
• 230 meters
• 240 meters

Explanation:

Step1: Find Stefano's elevation

Stefano's elevation is the initial height of the sunglasses. When \(t = 0\), \(h(0)=10\) meters.

Step2: Find the climber's elevation

The climber's elevation is the height of the sunglasses at \(t = 6\) seconds. From the table, when \(t = 6\), \(h(6)=- 166.4\) meters.

Step3: Calculate the difference in elevation

The difference \(d\) is \(d=10-(-166.4)\). Using the rule \(a - (-b)=a + b\), we have \(d = 10+166.4=176.4\approx176\) meters.

Answer:

176 meters