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
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
