Explain the purpose of the `Application` scope in ColdFusion and provide a scenario where it would be most useful.

The `Application` scope in ColdFusion provides a persistent storage area for variables that are accessible throughout the entire lifecycle of a ColdFusion application. Unlike other scopes like `Request`, `Session`, or `Form`, which are tied to a single request, a user's session, or a submitted form respectively, the `Application` scope exists for as long as the ColdFusion application is running. This means variables set in the `Application` scope retain their values even after multiple requests from the same user or different users. The `Application` scope is managed by the ColdFusion server, not by individual pages.

To access variables within the `Application` scope, you use the `application` keyword followed by the variable name. For example, `application.myVariable = “someValue”` sets a variable named `myVariable` within the `Application` scope to the value “someValue”. Subsequent code, regardless of the page or user, can then access this value using `application.myVariable`. The `Application` scope is initialized only once when the ColdFusion application starts. Any variables not previously defined are automatically created when first assigned a value. If the ColdFusion application is restarted, the contents of the `Application` scope are lost, as it is tied to the application's runtime instance.

A common scenario where the `Application` scope is particularly useful is for storing global configuration settings or application-wide counters. Consider an e-commerce application that needs to track the total number of orders placed. Instead of storing this count in a database or recalculating it on every page load, you can store it in the `Application` scope. For example:

```cfml
<cfscript>
if (isDefined("application.totalOrders")) {
application.totalOrders++;
} else {
application.totalOrders = 1;
}
</cfscript>
```

In this example, the code checks if `application.totalOrders` already exists. If it does, it increments the value. If it doesn't, it initializes `application.totalOrders` to 1. This ensures that the total order count is accurately maintained across all requests to the application. Another example would be storing a list of valid user roles, API keys, or other data that needs to be consistently available across the entire application without requiring database queries or session variables. The `Application` scope provides a centralized and persistent location for this type of global data.