The atmospheric pressure P in pounds per square inch(psi) is given by the formula below. Where "a" is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi=5,280 ft. round answer to the nearest foot)
P=14.7e^-.21a

Question

The atmospheric pressure P in pounds per square inch(psi) is given by the formula below. Where "a" is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi=5,280 ft. round answer to the nearest foot)
P=14.7e^-.21a

tkhunny · Answer

$$P = 14.7e^{-0.21a}$$  Solve for 'a' $$13.25 = 14.7e^{-0.21a}$$

anonymous · Answer

yes that is how I set up the problem, do I subtract 14.7 from both sides?

tkhunny · Answer

How is 14.7 "attached" to the rest of the expression involving 'a'?  Is it addition or subtraction?  NO.  It is multiplication.  Thus, division is called for.

anonymous · Answer

I am not sure the formula I have to use is p=14.7e^-0.21so do you take and subtract one side from the other then divide to find a?

tkhunny · Answer

You will need a logarithm.  Are you familiar with logarithms?

anonymous · Answer

yes, will i have to find the natural logarithm of -0.21 to find my answer?

tkhunny · Answer

It may appear so, but no, not in this one.  $$13.25 = 14.7e^{-0.21a}$$ Divide by 14.7 $$0.9013605442 = e^{-0.21a}$$ Now the Natural Logarithm $$ln(0.9013605442) = -0.1038499414 = -0.21a$$ divide by -0.21 and you are done.

That wasn't too bad, right?

anonymous · Answer

ok I think I understand...up to the middle... the 0.1038499414 I subtract from the ln then divide by -0.21? Im sorry I guess my brain isn't working well tonight..ok wait.... i divided the -0.1038499414 by -0.21 and got  0.494523531 so then i subtract that from 5,280ft?

tkhunny · Answer

Hmmm...  Maybe.  This, "subtract from the ln" doesn't actually mean anything, so I cannot be particularly confident that you are on the right track.

This part

ln(0.9013605442) = −0.1038499414

was only an evaluation of the logarithm of htat value inside the logarithm argument.

anonymous · Answer

yes i figured that out doing the calculations myself lol.... i finally seen where you go that

anonymous · Answer

Ok so I rof 0n answer of 0.494523529 but it etha tells me that 1 mile is 5280 this is wher I get confused again.do I divide my answer by5280? when I do that I get 9.365975928 I don't know how to ge the sea level

anonymous · Answer

please message me, thank you

tkhunny · Answer

We have a = 0.494523529.  Just take a good, hard look at this value.  It's about 1/2, right?  So, about 1/2 mile is the right answer.

5280 ft * 0.494523529 = ??  Done.