Sociologists have found that crime rates are infulenced by temperature. In a tow

Question

Sociologists have found that crime rates are infulenced by temperature. In a town of 100,000 people, the arime rate has been approximateod as CT-60 110, 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 bycrime(s) per month. (Simplify your answer.)

Explanation / Answer

Solution:

Given that

C = 1/5 (T - 60)2 + 110

C = 1/5 (T - 60)2 + 110

C = (1/5 (T- 60)2) + 110

dT/dt = 9 degrees/ month

Rate of crime = dC/dt = (1/5)(2)(T 60)(dT/dt) ................t is time in months

dC/dt = 9*9*2/5 =32.4 Crimes per month.

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