Sociologists have found that crime rates are influenced by temperature. In a town of $200,000$ people, the crime rate has been approximated as C$=1/10($T$-65)^2+100$ where C is the number of crimes per month and T is the average monthly temperature in degrees Fahrenheit. The average temperature for May was $77^$ and by the end of May the temperature was rising at the rate of $9^$ per month. How fast is the crime rate rising at the end of May? At the end of May, the crime rate is rising by crime$($s$)$ per month. $($Simplify your answer.$)$