Question

Suppose that a certain television program has an average point rating of 5.3 (ratings measure the number of viewers), and that the program's executives estimate that a 0.2 drop in the ratings will correspond to a dollar-sign ⁢ 4.1 million drop in revenue. If f left-parenthesis p right-parenthesis is the revenue earned in millions of dollars in terms of p, the ratings points, express this estimation as a derivative.

Answer 1

Answer:20.5

Explanation:

I you consider than there is a linear reltionship between p and f, then
`f(p)=a+b*p`

then, you need to fin out the value of b, and you know that:
`f(5.3)-f(5.3-0.2)=4.1\\f(5.3)-f(5.1)=4.1\\(a+b*5.3)-(a+b*5.1)=4.1\\a+b*5.3-a-b*5.1=4..1\\a-a+5.3b-5.1b=4.1\\0.2b=4.1\\b=4.1/0.2\\b=20,5`

Then f(p)=a+20.5p

And the derivative, f' which represent the variation rate is b=20.5

Because the derivative of a+nx is b