Sociologists have found that crime rates are influenced by temperature. In a tow
ID: 2886730 • Letter: S
Question
Sociologists have found that crime rates are influenced by temperature. In a town of 200,000 people, the crime rate has been approxitd asCT-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 8° per month. How fast is the crime rate rising at the end of May? (-65% + 100, where C is the number of crimes per At the end of May, the crime rate is rising bycrimets) per month (Simplify your answer.)Explanation / Answer
A) C=(1/10)*(T?65)2+10?0
dC/dt = (1/10)*(2)(T?65)(dT/dt) ... t is time in months , T=770 and dT/dt=80/month
dC/dt = (2/10)(77-65)(8) = 19.2 crimes per month
B)
C=(1/5)*(T?60)2+110
dC/dt = (1/5)*(2)(T?60)(dT/dt) ... t is time in months , T=770 and dT/dt=60/month
dC/dt = (2/5)(77-60)(6) = 40.8 crimes per month
C)
C=(1/5)*(T?65)2+110
dC/dt = (1/5)*(2)(T?65)(dT/dt) ... t is time in months , T=740 and dT/dt=90/month
dC/dt = (2/5)*(74-65)(9) = 32.4 crimes per month