Question

A balloon is released from a height of 10 feet. The balloon climbs an additional 70% of its previous height as each minute passes. Identify the geometric sequence that identifies the height at the fourth minute in bold (to the nearest tenth).

Answer 1

By the given scenario above and the condition that the height is increased by 70% every minute. The equation that would relate the number and the time, we have the equation,

H = (Hi)(1.70)^(t)

Substituting the known values,
H2 = (10 ft)*(1.70^4)
H2 = 83.521 ft

Answer: 83.521 ft

Answer 2

The initial height of the balloon is 10 feet which then increases by 70% to (10 ×1.7) = 17 feet, then to (17 × 1.7) =28.9 feet, and so fourth if the rate of increase is kept constant. Therefore, forming a geometric sequence such that to get any term in the sequence we use the formula ar∧(n-1), where a is the first term, r is the common ratio, and n is the term in the sequence. In this case a is 10 and r= 1.7 , to get the height in the fourth minute it means n =5 (for the first term there is 0 minutes, such that for 0 minutes n= 1)
Thus, 10 × 1.7 ∧ 4 = 83.521 feet.
Therefore, the answer is 83.521 feet