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

Question

Sociologists have found that crime rates are influenced by temperature. In a town of 150, 000 people, the crime rate has been approximated as C = 1/5(T - 60)^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 71 degree and by the end of May the temperature was rising at the rate of 6 degree 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)

Explanation / Answer

We have given C=1/5(T-60)2+100

differentiating with respect to m

dC/dm=(1/5)(2*(T-60))dT/dm

we have given The average temperature May was T=710F and dT/dm=60

substitute above value inot dC/dm

dC/dm=(1/5)(2*(71-60))*6

dC/dm =1/5*(2*6*9)=21.6

At the end of the May,the crime rate is rising by approximately 22 crime(s) per month

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