Looking on the internet deeply has found these results:

I appreciate you taking the time to consider my application. is the most popular phrase on the web.

I appreciate your taking the time to consider my application. 18 results on the web	I appreciate you taking the time to consider my application. 1416 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
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I appreciate your taking the time to consider my application.

18 results on the web

I appreciate you taking the time to consider my application.

1416 results on the web

More popular!

I appreciate you taking the time to talk to me.
I appreciate you taking the time to consider a stay at all.
Mr. Beecher, l appreciate your taking the time to see me.
We appreciate your taking the time to be here with us today.
I appreciate you taking the time to see me.
I appreciate your taking the time to see us, Dr. Grey, But I promised Isobel's algebra ii teacher That I'd have her back in time for fifth period.
I appreciate your taking the time.
I appreciate you taking the time to... answer my questions.