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First note that the answer is not ``we lose two grams every hundred years so '' The rate of decay depends on the amount of material present That is the key Instead, we let R( t) denote the amount of radioactive material at time t Equation ( ) guarantees that R has the form R( t) = P eK t Letting t = 0 denote the time at which there are 5 grams of isotope, and measuring time in years, we have R( 0) = 5 and R( 100) = 3 From the first piece of information we learn that 5 = P eK 0 = P Hence P = 5 and R( t) = 5 eK t = 5 ( eK ) t The second piece of information yields 3 = R( 100) = 5 ( eK ) 100 We conclude that ( eK ) 100 = 3 5

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// Signal the event mreSet(); } } class ManualEventDemo { static void Main() { ManualResetEvent evtObj = new ManualResetEvent(false); MyThread mt1 = new MyThread("Event Thread 1", evtObj); ConsoleWriteLine("Main thread waiting for event");

// Wait for signaled event evtObjWaitOne(); ConsoleWriteLine("Main thread received first event");

// Reset the event evtObjReset();

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mt1 = new MyThread("Event Thread 2", evtObj); // Wait for signaled event evtObjWaitOne(); ConsoleWriteLine("Main thread received second event"); } }

The output is shown here (The actual output you see may vary slightly)

Inside thread Event Thread 1 Event Thread 1 Main thread waiting for event Event Thread 1 Event Thread 1 Event Thread 1 Event Thread 1 Event Thread 1 Done! Main thread received first event Inside thread Event Thread 2 Event Thread 2 Event Thread 2 Event Thread 2 Event Thread 2 Event Thread 2 Event Thread 2 Done! Main thread received second event

Thus the formula for the amount of isotope present at time t is R( t) = 5 3 5

First, notice that MyThread is passed a ManualResetEvent in its constructor When MyThread s Run( ) method finishes, it calls Set( ) on that event object, which puts the

After looking thoroughly at your reports on last month s sales calls describing who you saw and what objections to closing the sales were raised, and reviewing those special and extraordinary events such as the blizzard in the upper Midwest, as well as standard events such as President s Day, there seems to be no clear or de nitive reason why sales are down

Part II:

event object into a signaled state Inside Main( ), a ManualResetEvent called evtObj is created with an initially unsignaled state Then, a MyThread instance is created and passed evtObj Next, the main thread waits on the event object Because the initial state of evtObj is not signaled, this causes the main thread to wait until the instance of MyThread calls Set( ), which puts evtObj into a signaled state This allows the main thread to run again Then the event is reset and the process is repeated for the second thread Without the use of the event object, all threads would have run simultaneously and their output would have been jumbled To verify this, try commenting out the call to WaitOne( ) inside Main( ) In the preceding program, if an AutoResetEvent object rather than a ManualResetEvent object were used, then the call to Reset( ) in Main( ) would not be necessary The reason is that the event is automatically set to a non-signaled state when a thread waiting on the event is resumed To try this, simply change all references to ManualResetEvent to AutoResetEvent and remove the calls to Reset( ) This version will execute the same as before

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One other class that is related to synchronization is Interlocked This class offers an alternative to the other synchronization features when all you need to do is change the value of a shared variable The methods provided by Interlocked guarantee that their operation is performed as a single, uninterruptable operation Thus, no other synchronization is needed Interlocked provides static methods that add two integers, increment an integer, decrement an integer, compare and set an object, exchange objects, and obtain a 64-bit value All of these operations take place without interruption The following program demonstrates two Interlocked methods: Increment( ) and Decrement( ) Here are the forms of these methods that will be used: public static int Increment(ref int location) public static int Decrement(ref int location) Here, location is the variable to be incremented or decremented

// Use Interlocked operations using System; using SystemThreading; // A shared resource class SharedRes { public static int Count = 0; } // This thread increments SharedResCount class IncThread { public Thread Thrd; public IncThread(string name) { Thrd = new Thread(thisRun); ThrdName = name;

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