When Covington Mayor Kim Carter took office in 2008, she wanted to run the city more like a business. She’s had to, as the city in her tenure has responded to the economic downturn by slashing its budget $20 million and cutting 35 positions through early retirement and not filling vacant positions. Even with the reductions, the city has had many accomplishments, and it has plans for the future, Carter said Thursday in her state of the city address at the Turner Lake Complex.