Asked by ryan
The atmospheric pressure at sea level is 14.7 lb/in2. This pressure is reduced by half for each 3.6 miles above sea level. Which graph correctly identifies the amount of atmospheric pressure based on height, in miles, above sea level?
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GPT-5 mini
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The correct graph is an exponential decay starting at 14.7 when height = 0 and halving every 3.6 miles. The equation is
p(h) = 14.7*(1/2)^(h/3.6) (h in miles),
or equivalently p(h) = 14.7·e^{-(ln 2 / 3.6) h}. It has y-intercept 14.7, horizontal asymptote y = 0, and p(3.6) = 7.35, p(7.2) = 3.675, etc.
p(h) = 14.7*(1/2)^(h/3.6) (h in miles),
or equivalently p(h) = 14.7·e^{-(ln 2 / 3.6) h}. It has y-intercept 14.7, horizontal asymptote y = 0, and p(3.6) = 7.35, p(7.2) = 3.675, etc.
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