Question

What answer would this be? Question is attached

Answer 1

0.65m

Explanation:

Given the function as

`P(h)=P_0*e^(-0.00012h)`

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

`P_0=x`

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

`P(h)=(65)/(100) *x=0.65x`

The function will be

`0.65x(h)=x*e^(-0.00012h)`

Divide both sides by x

`0.65=e^(-0.00012h)\\ \\\\e=2.71828182846\\\\\\0.65=2.7182818284^(-0.00012h) \\\\\\0.65=0.99989h\\\\\\(0.65)/(0.99989) =(0.99989h)/(0.99989) \\\\\\h=0.65m`

Answer 2

Option: A is the correct answer.

A. 3589.9 m

Explanation:

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

`P(h)=P_0\cdot e^(-0.00012h)`

where
`P_0` 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.

`P_0\cdot e^(-0.00012h)=0.65\cdot P_0\\\\i.e.\\\\e^(-0.00012h)=0.65\\\\i.e.\\\\e^(0.00012h)=(1)/(0.65)\\\\i.e.\\\\\ln(e^(0.00012h)}=\ln((1)/(0.65))\\\\i.e.\\\\0.00012h=\ln((1)/(0.65))\\\\i.e.\\\\h=3589.8576\ m`

which is approximately equal to:

`h=3589.9\ m`