Question
the atmosphere pressure P in pounds per square inch (psi) is given by
P=14.7e upper o.21a where a is the attitude above sea level in miles. If a city has an atmosphere pressure y 13.29 psi what is its altitude. Recall that one mile = 5,280 feet. Round to the nearest feet
P=14.7e upper o.21a where a is the attitude above sea level in miles. If a city has an atmosphere pressure y 13.29 psi what is its altitude. Recall that one mile = 5,280 feet. Round to the nearest feet
Answers
I suspect the equation should read
P = 14.7e<sup>-0.21a</sup>
in order that the pressure decreases with altitude.
For P=13.29
13.29=14.7<sup>0.21a</sup>
e<sup>0.21a</sup> = 13.29/14.7
take log on both sides
-0.21a = ln(13.29/14.7)
a=-ln(13.29/14.7)/0.21
= 0.4802 miles
= 2535.3 feet (approx.)
= 2535 feet (approx.)
P = 14.7e<sup>-0.21a</sup>
in order that the pressure decreases with altitude.
For P=13.29
13.29=14.7<sup>0.21a</sup>
e<sup>0.21a</sup> = 13.29/14.7
take log on both sides
-0.21a = ln(13.29/14.7)
a=-ln(13.29/14.7)/0.21
= 0.4802 miles
= 2535.3 feet (approx.)
= 2535 feet (approx.)
13.29 = 14.7 e^(.21a)
.90408.. = e^(.21a)
by rules of logs
.21a = ln .90408...
.21a = -.0100835..
a = -.48016 miles
or - 2535 ft below sealevel !!!!!!!
Wow, since the lowest point in North America, Death Valley is only about 260 ft below sea level, you city is a mystery.
... or else your equation is bogus.
.90408.. = e^(.21a)
by rules of logs
.21a = ln .90408...
.21a = -.0100835..
a = -.48016 miles
or - 2535 ft below sealevel !!!!!!!
Wow, since the lowest point in North America, Death Valley is only about 260 ft below sea level, you city is a mystery.
... or else your equation is bogus.
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