Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below.
P(h)=Po*e^-0.00012h
In this function, Po is the air pressure at the surface of the Earth, and h is the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 65% of the air pressure at the surface of the Earth?

A. .65m
B. 3587.4m
C. 3589.9m
D. 5416.7m

Question

Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below.
P(h)=Po*e^-0.00012h
In this function, Po is the air pressure at the surface of the Earth, and h is the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 65% of the air pressure at the surface of the Earth?

A. .65m
B. 3587.4m
C. 3589.9m
D. 5416.7m

anonymous · Answer

@ranga do you think you could help me with this problem please?

anonymous · Answer

0.65=e^-0.00012h

ln(0.65)=ln(e^-0.00012h)

ln(0.65)=-0.00012h

h=ln(0.65)/-0.00012

anonymous · Answer

ln(e^x)=x

anonymous · Answer

I'm sorry @dhouser , but how exactly would I solve that?

anonymous · Answer

Would I just divide .65 by -.00012?

shamil98 · Answer

ln means the natural log
take the natural of (0.65) first. then divide it

shamil98 · Answer

Punching that into your calculator you get 3589.86
rounding to the tenth 3589.9

anonymous · Answer

wouldn't it be negative because I divide ln(.65) by -.00012? thats what Dhouser told me earlier so I'm not sure :o

shamil98 · Answer

i'm not sure the exact mechanics but it turns out to be positive

ranga · Answer

ln(.65) will be negative.

anonymous · Answer

oh but ln(.65) divided by -.00012 would be positive 3589.9 like shamil said, correct?

ranga · Answer

yes.

shamil98 · Answer

yeah negative/negative  = positive

anonymous · Answer

woohoo! thanks y'all :)