Problema Solution
As a hot-air balloon rises, the air cools. If the air is not re-heated, the balloon rises more slowly with each minute of flight. Suppose after one minute, a hot air balloon rises 120 feet. in each succeeding minute, the balloon rises only 60% as far as it rose in the previous minute. How far will the balloon rise in 8 minutes? a)302.34 ft b)294.96 ft c)199.87 ft d)117.38 ft
Answer provided by our tutors
After 1 min the balloon is at a height of: 120 ft
After 2 min the balloon is at a height of: 120 + 0.60*120
After 3 min the balloon is at a height of: 120 + 0.60*120 + 0.60* 0.60*120
........
After 8 min the balloon is at a height of: 120 + 0.60*120 + (0.60^2)*120 + (0.60^3)*120...(0.60^7)*120
120 + 0.60*120 + (0.60^2)*120 + (0.60^3)*120...(0.60^7)*120 =
= 120(1 + 0.60 + 0.60^2 + ... +0.60^7) = 120(1 - 0.60^8)/(1 - 0.6) =
= 294.96
In the solution we used the formula for the sum of the first 8 member of the Geometric Sequence: 1, 0.6, 0.6^2, 0.6^3...
The answer is b)294.96 ft.