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).

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

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