Identify first instance of a value in a list

Hi,
I've come across an issue that I really need some help with. I've got some data which follows an upwards trend but with a high frequency oscillation on top of the signal (due to noise in the measurement equipment). I'd like to look at the signal and identify the first instance when the data in column A reaches 13 and return the corresponding value in column B.

I've tried using a LOOKUP but if my array is substantially large then the LOOKUP doesn't seem able to identify the correct cell. I'm stuck with using a large array as the worksheet is used to process many sets of data and the data can shift around so the array needs to be large enough to always capture up to the point where the data passes 13.

Are there any alternative ways of doing this which will give me the correct result?

I've attached some sample data and my LOOKUP result to this post. By scrolling through the data I can see that Column A reaches 13 in cell A241 however the LOOKUP seems to be returning the values from row 266.

Any help would be massively appreciated!

Thank you,

Alasdair

Test.xls

A simple way would be to use a helper column, say Column C
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I avoided using an array formula because it was indicated that the data range was large, and other calculations have to be performed.
Generally speaking, in my opinion, avoiding arrays in large sheets is preferable, they can at times slow a workbook dramatically.

However this Dynamic version of Cutters' formula might be useful,it only calculates the used rows,and the data can be any length.
In E2

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