Need help with Maths

you plug in the numbers and later write how much are k and h. then you state the law with correct constants. Lastly you plug in 10000m

>>84083
tats wrog

>>84092
How do I do it then?
Looking at it, I think it uses natural logs, but I dun know how to do it.

>>84079
>>84105

I will use exp(x) to represent e^x, for convenience.

What we can do is find the constants a and k using two data points, and then show the rest of the data points follow the law we come up with.

Let (h1, P1) and (h2, P2) be pairs of height and pressure. Then we have

(1) P1 = a*exp(k*h1)
(2) P2 = a*exp(k*h2)

Now rearrange equation 1 to obtain:

(1) a = P1/exp(k*h1)
(1) a = P1*exp(-k*h1)

And substitute into equation 2:

(2) P2 = P1*exp(-k*h1)*exp(k*h2)
(2) P2 = P1*exp(k*h2 - k*h1)
(2) P2/P1 = exp(k*(h2-h1))
(2) ln(P2/P1) = k*(h2-h1)
(2) ln(P2/P1)/(h2-h1) = k

Now we have only k in terms of known information. After k has been calculated, use it in equation 1 to calculate a.

Now we have a relationship between h and P. Plug various heights into the relation and verify the pressures you get out to verify the relation is correct. Then, use the relation to predict what the pressure at 10000m would be.

File: error.png (43KB, 533x487px) Image search: [Google]

43KB, 533x487px

>>84121
Sorry for the late response, but I couldn't follow your advice until right now.
I tried putting in the numbers, but I think I'm not understanding it properly since I'm not getting an accurate a value.
Could you please check over my working and see where I went wrong?

>>84255
Scratch that, just checked my answers in the back of my textbook and apparently k=-7×10^(-5) and a=76.
Now I'm even more at a loss since I I don't understand how you reach those answers.

>>84255

This is where you went wrong:
>ln((68.42/73.439)/1000) = k

h2-h1 should not be in the log. That line should be:

ln(68.42/73.439)/1000 = k

This yields the correct answer you posted in >>84285

>>84298
Ah, I get it now. Thanks anon!