# How to find an asymptote of a logarithmic curve

An exponential decay curve has been plotted asymptoting at approximately x=30 (correct for what I am looking at)

How can I find the exact value from the curve? I was hoping to be able to use something similar to the FindMinimum function, or draw a line along the asymptote and find the intersection with the x-axis.

This is the function used to plot the curve:

    Plot[((5/Log[2])*Log[(80046.8 - ((0.79) (101325 + (1030*9.81*d))))/((313545. + 2.17341d) - ((0.79) (101325 + (1030*9.81*d))))]), {d, 0, 60}, AxesLabel -> {Depth - m, Time - mins}]

• This site is for questions about the software Mathematica. Did you mean to ask this here, or at math.SE? Apr 19, 2013 at 13:52
• Yes, the curve has been plotted on mathematica
– emma
Apr 19, 2013 at 13:54
• Surely you can see that your question is underspecified. How and what do you plot? Yes, an exponential curve; but what do you do? Plot[1+Exp[-x/5],{x,0,50}]? something else? Try to be specific. Pretend that you don't know what you are doing; would you understand your explanation? If not, neither will we...
– acl
Apr 19, 2013 at 13:58
• A hint: Apply Rationalize[] to your function first, and then feed this to Limit[]: Limit[(* your function *), d -> ∞] Apr 19, 2013 at 14:18
• Try Series[(* your function *), {d, ∞, 2}]. Apr 19, 2013 at 14:41

The vertical asymptote is caused by the denominator of the Log function going through zero. Therefore, find the value of $d$ such that your denominator is zero.

Solve[(313545. + 2.17341 d - 0.79 (101325 + 1030*9.81*d)) == 0, d


The result is 29.259612511.