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Here are a few more related questions for practice:
1. How would the relationship between ratings and revenue change if we had a different scale for revenue loss?
2. If the rating increases by 0.2, how much revenue gain would that predict using the same derivative?
3. How could this derivative be used to predict long-term trends in revenue based on gradual changes in ratings?
4. What would happen if the drop in ratings was non-linear? How could we represent this using calculus?
5. Could we integrate the derivative to find the total revenue over a range of ratings?

Tip: In real-world scenarios, derivatives are often used to model how sensitive outcomes (like revenue) are to changes in measurable factors (like ratings).

On May 9, 2007, CBS Evening News had a 4.3 point rating. News executives estimated that a 0.1 drop in the ratings for CBS Evening News corresponds to a $5.5 million drop in revenue. Express this information as a derivative. Specify the function, the variables, the units, and the point at which the derivative is evaluated.

This problem explores how a 0.1 drop in CBS Evening News ratings corresponds to a $5.5 million drop in revenue. Learn how to express this as a derivative, specify the function, variables, and units, and evaluate the derivative at a given point. Suitable for students in Grades 11-12.

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