the function $f(x)=-158.8x^{2}+2469.9x + 3010.5$ models the dvd sales, in billions of dollars, from 1999 to…

the function $f(x)=-158.8x^{2}+2469.9x + 3010.5$ models the dvd sales, in billions of dollars, from 1999 to 2017, where $x$ is the number of years since 1999. what is the average rate of change of dvd sales, in billion of dollars, per year for the period from 2001 to 2008? round your answer to the nearest tenth, if necessary.

the function $f(x)=-158.8x^{2}+2469.9x + 3010.5$ models the dvd sales, in billions of dollars, from 1999 to 2017, where $x$ is the number of years since 1999. what is the average rate of change of dvd sales, in billion of dollars, per year for the period from 2001 to 2008? round your answer to the nearest tenth, if necessary.

Answer

Explanation:

Step1: Find the value of (x) for 2001 and 2008

For 2001, (x = 2001 - 1999=2). For 2008, (x = 2008 - 1999 = 9).

Step2: Calculate (f(2))

Substitute (x = 2) into (f(x)=-158.8x^{2}+2469.9x + 3010.5). [ \begin{align*} f(2)&=-158.8\times2^{2}+2469.9\times2 + 3010.5\ &=-158.8\times4+4939.8+3010.5\ &=-635.2+4939.8 + 3010.5\ &=7315.1 \end{align*} ]

Step3: Calculate (f(9))

Substitute (x = 9) into (f(x)=-158.8x^{2}+2469.9x + 3010.5). [ \begin{align*} f(9)&=-158.8\times9^{2}+2469.9\times9+3010.5\ &=-158.8\times81 + 22229.1+3010.5\ &=-12862.8+22229.1+3010.5\ &=12376.8 \end{align*} ]

Step4: Calculate the average rate of change

The formula for the average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 2), (b = 9). [ \begin{align*} \frac{f(9)-f(2)}{9 - 2}&=\frac{12376.8-7315.1}{7}\ &=\frac{5061.7}{7}\ &=723.1 \end{align*} ]

Answer:

(723.1)