Respuesta :

lucic

Answer:

0.65m

Step-by-step explanation:

Given the function as

[tex]P(h)=P_0*e^{-0.00012h}[/tex]

Lets take the air pressure at the surface of the Earth to be x

[tex]P_0=x[/tex]

Then 65% of this will be the air pressure P(h)

[tex]P(h)=\frac{65}{100} *x=0.65x[/tex]

The function will be

[tex]0.65x(h)=x*e^{-0.00012h}[/tex]

Divide both sides by x

[tex]0.65=e^{-0.00012h}\\ \\\\e=2.71828182846\\\\\\0.65=2.7182818284^{-0.00012h} \\\\\\0.65=0.99989h\\\\\\\frac{0.65}{0.99989} =\frac{0.99989h}{0.99989} \\\\\\h=0.65m[/tex]

Answer:

Option: A is the correct answer.

                     A.   3589.9 m

Step-by-step explanation:

The function which determines the pressure h height above the surface of earth is:

[tex]P(h)=P_0\cdot e^{-0.00012h}[/tex]

where [tex]P_0[/tex] is the pressure at the surface of the earth.

We are asked to find the height when the pressure above the surface of earth is equal to 65% of the pressure at the surface of earth.

i.e.

[tex]P_0\cdot e^{-0.00012h}=0.65\cdot P_0\\\\i.e.\\\\e^{-0.00012h}=0.65\\\\i.e.\\\\e^{0.00012h}=\dfrac{1}{0.65}\\\\i.e.\\\\\ln(e^{0.00012h}}=\ln(\dfrac{1}{0.65})\\\\i.e.\\\\0.00012h=\ln(\dfrac{1}{0.65})\\\\i.e.\\\\h=3589.8576\ m[/tex]

which is approximately equal to:

[tex]h=3589.9\ m[/tex]

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