A balloon takes 1 minute to rise 60 feet in the air. each minute after that, the balloon rises 40% as far as it did the previous minute. which equation represents the total distance, d, in feet that the balloon rises in 6 minutes?

Answers

Answer 1

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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Answer 2

Answer:

B

Explanation:


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