All you have to do for part a) is think about what this phrase means. After that you can have a shot at solving b)M ... increases at a rate proportional to the reciprocal of x,
1) Earthquake magnitude M, as measured on the Richter scale, increases at a rate proportional to the reciprocal of x, where x is the normalized seismograph reading, measured in millimeters.
a) Write the equation for M'(x)
b) Find a general formula for M(x). (The formula should contain two undetermined constants.)
-I have no idea how I should go about solving this problem. Please help.
Remember, when you say that "y is proportional to x", you are saying that y=kx, for some constant k (called the constant of proportionality). So if the rate of increase of M is proportional to the inverse of x, it means for some constant k.
--Kevin C.
No. You need to perform the integration before you substitute in (although writing this is making me wonder why. oh well)
M = [tex]k\int(1/x)dx[\MATH]
M = k log|x| + c
then you can substitute and I am sure you will be able to solve for one of the values.