The atmospheric pressure P in pounds per square inch (psi) is given by P = 14.7 e−0.21 a where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.33 psi, what is its altitude?

Question

whpalmer4 · Answer

$$P = 14.7e^{-0.21a} = 13.33$$
Shuffle the equation so you have $e^{-0.21a}$ alone on the left.  Take the natural log of both sides, and remember that $$\ln e^x = x$$.

anonymous · Answer

thanx but i still dont understand

whpalmer4 · Answer

Well, tell me what you don't understand, and we'll walk through it.

anonymous · Answer

I get P=1.7e^-.21^a
13.33psi =14.7e^.21^a
then i am lost

whpalmer4 · Answer

The exponent on e is $-0.21a$ $$13.33 = 14.7e^{-0.21a}$$We'll divide both sides by 14.7: $$\frac{13.33}{14.7} = e^{-0.21a}$$Now we take the natural log of both sides: $$\ln \frac{13.33}{14.7} = \ln e^{-0.21a}$$But as I pointed out above, in the expression on the right, the natural log of e raised to the is just . $$\ln \frac{13.33}{14.7} = -0.21a $$ Now solve that for $a$ and fire up your calculator to find the value of $a$

anonymous · Answer

i get 4070 but thats not right

whpalmer4 · Answer

Okay, what do you get for 13.33 / 14.7?

anonymous · Answer

0.906802721

whpalmer4 · Answer

Good.   take the natural log of that, what do you get?

anonymous · Answer

i am not sure what the natural log is

whpalmer4 · Answer

do you have a button labeled LN or ln on your calculator?

whpalmer4 · Answer

if not, what brand/model calculator do you have?

anonymous · Answer

just a basic

whpalmer4 · Answer

just + - x / ?

anonymous · Answer

??

whpalmer4 · Answer

Do you have functions besides + - x / ? There's a web calculator you can use at http://web2.0calc.com/

anonymous · Answer

1561 ft ?

whpalmer4 · Answer

No, the answer is going to be in miles.

What's the equation you are trying to evaluate?  I asked to solve for a, but you didn't tell me what you got for an equation...

anonymous · Answer

The atmospheric pressure P in pounds per square inch (psi) is given by
P = 14.7 e−0.21 a
where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.33 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
3975 

 ft

anonymous · Answer

the 3975 doesnt belong

anonymous · Answer

this is the question

anonymous · Answer

hello?????

whpalmer4 · Answer

Okay, in that web calculator, divide 13.33 by 14.7.  Then move the mouse cursor down below the button labeled "log" and some more buttons should appear, one of them being "ln".  Click on that button.  Then click on the division button, and then the +- button (right underneath the 2 button) and 0.21, then press the = button.  You should get 0.465858...which is your answer in miles.  Multiply it by 5280 to get your answer in feet.  If the first digit to right of the decimal point is 5,6,7,8 or 9, round up, otherwise round down.

anonymous · Answer

2460

whpalmer4 · Answer

That's what I get as well.

anonymous · Answer

ok thank you