# Thread: Reducing exponential laws to linear form????

1. ## Reducing exponential laws to linear form????

Hi folks!
I was wondering if any kind people out there could work throught the following question and explain for me as i must admit i am lost!!

atmosperic pressure p is measured at varying altitudes h and the results are shown below:

Altitude h m pressure p cm
500 73.39
1500 68.42
3000 61.60
5000 53.56
8000 43.41

show that the quantities are related by the law p = a e(to the power of little k and little h) kh
where a and k are constants. Determine the values of a and k and state the law. also find the atmospheric pressure at 10,000m

if you can help i will bow down to thee! :-)

Thanks

Hi folks!
I was wondering if any kind people out there could work throught the following question and explain for me as i must admit i am lost!!

atmosperic pressure p is measured at varying altitudes h and the results are shown below:

Altitude h m pressure p cm
500 73.39
1500 68.42
3000 61.60
5000 53.56
8000 43.41

show that the quantities are related by the law p = a e(to the power of little k and little h) kh
where a and k are constants. Determine the values of a and k and state the law. also find the atmospheric pressure at 10,000m

if you can help i will bow down to thee! :-)

Thanks

$P = Ae^{kh}$

Take logs of both side:

$ln(P) = ln(Ae^{kh}) = ln(A) + ln(e^{kh}) = kh + ln(A)$

Note how similar this is to the equation of a straight line (y = mx +c) ?

Plotting ln(P) against h gives a gradient of k and y-intercept of ln(A).