Air Pressure and altitude -drivitives HELP!!!!

[zeus123]

Can anybody help me with these I am stumped on these questions.

Air Pressure at sea level is 30 inches of mercury. At an altitude of h feet above see level, the air pressure, P, in inches of mercury, is given by
P=30e^-3.32*10-5h

A. Sketch a graph of P against h.

B. Find the equation of the tangent line at h=0.

C. A rule of thumb used by travelers is that air pressure drops about 1 inch for every 1000 foot increase in height above sea level. Write a formula for; the air pressure given by this rule of thumb.

D. What do you notice about the relation to you answers to parts B and C?

E. Compare both methods and determine the heights at which the rule of thumb is fairly accurate and the heights at which the rule of thumb become less accurate.

 

[Deleted member 4993]

Can anybody help me with these I am stumped on these questions.

Air Pressure at sea level is 30 inches of mercury. At an altitude of h feet above see level, the air pressure, P, in inches of mercury, is given by
P=30e^-3.32*10-5h

A. Sketch a graph of P against h.

B. Find the equation of the tangent line at h=0.

C. A rule of thumb used by travelers is that air pressure drops about 1 inch for every 1000 foot increase in height above sea level. Write a formula for; the air pressure given by this rule of thumb.

D. What do you notice about the relation to you answers to parts B and C?

E. Compare both methods and determine the heights at which the rule of thumb is fairly accurate and the heights at which the rule of thumb become less accurate.

I think your equation is:

\(\displaystyle \displaystyle P \ = \ 30 * e^{3.32*10^{-5}*h}\)

The question asks you to plot P vs. h - so do it. (If I were to plot this - I would plot ln(P) as dependent variable and h as the independent variable.).

What is the value of P at h= 0? What is the slope of tangent line at h = 0?

Where are you stuck?

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[DrPhil]

Can anybody help me with these I am stumped on these questions.

Air Pressure at sea level is 30 inches of mercury. At an altitude of h feet above see level, the air pressure, P, in inches of mercury, is given by
P=30e^-3.32*10-5h

A. Sketch a graph of P against h.

B. Find the equation of the tangent line at h=0.

C. A rule of thumb used by travelers is that air pressure drops about 1 inch for every 1000 foot increase in height above sea level. Write a formula for; the air pressure given by this rule of thumb.

D. What do you notice about the relation to you answers to parts B and C?

E. Compare both methods and determine the heights at which the rule of thumb is fairly accurate and the heights at which the rule of thumb become less accurate.

Writing algebraid expressions inline requires that you use extra parentheses to show the order of operations. At h=0, the formula should reduce to 30 (with units "inch Hg"). I can't see what order of operations gives that.

Show us your work! That may clarify.

BTW, I live at an elevation of 7600 feet, and up here the pressure is about 22.2 inches Hg.

EDIT: having seen the response by Subhotosh Kahn, I think his formula looks right except exponent has to be negative:

\(\displaystyle \displaystyle P = (30\ \mathrm{inch Hg}) * e^{- (3.32×10^{-5}/\mathrm{foot})\ h}\)