Question

A bike tire just ran over a nail and it is losing pressure at a rate of 10% every minute the tire pressure is currently 1464 kPa what will it be in 10 minutes

Answer 1

Correct answer: p = 510.465 kPa

Explanation:

Initial pressure p = 1,464 kPa

after one minute p₁ = 1,464 · 0.9

after two minutes p₂ = p₁ · 0.9 = (1,464 · 0.9) = 1,464 · 0.9²

after three minutes p₃ = p₂ · 0.9 = (1,464 · 0.9²) · 0.9 = 1,464 · 0.9³

.............................................................

after n minutes pₙ = 1,464 · 0.9ⁿ

in accordance with the foregoing

after ten minutes p₁₀ = 1,464 · 0.9¹⁰ = 1,464 · 0.3487 = 510.465 kPa

p₁₀ = 510.465 kPa

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