The equation represents the total distance, d, in feet that the balloon rises in 6 minutes [tex]d=\frac{60(1-0.4^6)}{1-0.4}[/tex].
Given that a balloon takes 1 min to rise 60 feet in the air each min after that it rises 40% as far as the previous minute
So it second minute it rises 40% x 60 feet (60 x 0.4)= 24 feet in 3rd minute it rises 40% x 24 feet = (24x0.4) = (60x0.42) feet
So in n-th minute it rises (60 x [tex]0.4^{n-1}[/tex]) feet
So total height d in n- minutes will be
d = 60 + (60 × 0.4) + (60 × 0.4²) + ... + (60 x 0.4"-1)
= 60[1 + 0.4 + 0.4² + ... + 0.4" 1]
[tex]=60 \times \frac{1-0.4^n}{1-0.4}[/tex]
here n=6
So it will rise to
[tex]d=\frac{60(1-0.4^6)}{1-0.4}[/tex]
Learn more about the equation here: https://brainly.com/question/2972832
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