gunnatvinson
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plz help me

The table shows the change in the annual sales turnover of a company in millions of dollars, S(x), where x represents the years since the company was founded.

x S(x)
1 $495
3 $598.95
5 $724.73
7 $876.92
9 $1,061.08

What is the predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11]?

A.
$184.15 per year
B.
$111.42 per year
C.
$222.83 per year
D.
$92.08 per year

Respuesta :

Answer:

its going to be d

Step-by-step explanation:

Answer:

The correct option is B.

Step-by-step explanation:

The general exponential regression model is

[tex]y=ab^x[/tex]

Using regression tool the exponential regression model for the given data is

[tex]S(x)=449.9999(1.09999)^x[/tex]

[tex]S(x)=450(1.1)^x[/tex]

The value of function at x=9 is

[tex]S(9)=450(1.1)^9=1061.07646[/tex]

The value of function at x=11 is

[tex]S(11)=450(1.1)^{11}=1283.90252[/tex]

The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is

[tex]m=\frac{S(11)-S(9)}{11-9}[/tex]

[tex]m=\frac{1283.90252-1061.07646-}{2}=111.413\approx 11.42[/tex]

The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is 11.42. Therefore the correct option is B.

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