The effectiveness of a police force may be measured by its clearance rate: the number of...

 

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The effectiveness of a police force may be measured by its clearance rate: the number of charges laid in a month divided by the total number of unsolved crimes. In Arachnid Boy's home town, new crimes are reported roughly 10 times per month, and while Arachnid boy is in town, the police clearance rate is 50%. Arachnid Boy comes back from his holiday and finds there are 140 unsolved crimes. Let a be the number of unsolved crimes at the start of month t, with t= 0 representing the first month that Arachnid Boy is back from his holiday. We can find an equation for a by solving the initial value problem dr crimes per month, and dt initially, a = . The solution to this inital value problem is 2= a GB As time drags on, the number of unsolved crimes approaches, to the nearest integer à P lim = t-x The effectiveness of a police force may be measured by its clearance rate: the number of charges laid in a month divided by the total number of unsolved crimes. In Arachnid Boy's home town, new crimes are reported roughly 10 times per month, and while Arachnid boy is in town, the police clearance rate is 50%. Arachnid Boy comes back from his holiday and finds there are 140 unsolved crimes. Let a be the number of unsolved crimes at the start of month t, with t= 0 representing the first month that Arachnid Boy is back from his holiday. We can find an equation for a by solving the initial value problem dr crimes per month, and dt initially, a = . The solution to this inital value problem is 2= a GB As time drags on, the number of unsolved crimes approaches, to the nearest integer à P lim = t-x