How do property taxes increase after I purchase a rental?

[Steve S.]

I'm considering buying a rental in the DFW area for about $300,000.  This duplex, per zillow, currently shows a property tax value of $195,000.  The home was built in 2005.  

If i acquire this property for $300,000, should I expect the property tax value of this property to increase very soon by over $100,000 to near or equal to the $300,000 I plan to pay for the property?

If not, what's a more realistic amount to model over the next 5-10 years of owning the property and renting it out?