Final Answer:
The height of the 7th boy is 1.93 meters.
Step-by-step explanation:
To find the height of the 7th boy, we need to use the formula provided in the question:
S = (343 - 343 × 1.4⁷) / (1 - 1.4)
First, we need to calculate the value of 1.4⁷:
1.4⁷ = 1.4 × 1.4 × 1.4 × 1.4 × 1.4 × 1.4 × 1.4 = 10.288
Now, we can calculate the value of S:
S = (343 - 343 × 10.288) / (1 - 1.4)
S = (343 - 3430.64) / 0.6
S = 343 - 3430.64 / 0.6
S = 343 - 5717.76
S = -2284.76
Now, we need to find the height of the 7th boy. We know that the height of the 4th boy is 43 centimeters, so we can use the formula:
height of 7th boy = height of 4th boy + (7 - 4) × height increment
height of 7th boy = 43 + (7 - 4) × 10
height of 7th boy = 43 + 3 × 10
height of 7th boy = 43 + 30
height of 7th boy = 73
Therefore, the height of the 7th boy is 1.93 meters (73 / 100).