the function f(x)=1.1x³ - 33x² + 260x + 564 below models the number of discharges from the military, f(x)…

the function f(x)=1.1x³ - 33x² + 260x + 564 below models the number of discharges from the military, f(x), of active - duty gay service members under the \dont ask, dont tell\ policy x years after 1994. complete parts a and b. a. find the slope of the secant line from x₁ = 0 to x₂ = 4. the slope of the secant line is . (round to the nearest whole number as needed.)

the function f(x)=1.1x³ - 33x² + 260x + 564 below models the number of discharges from the military, f(x), of active - duty gay service members under the \dont ask, dont tell\ policy x years after 1994. complete parts a and b. a. find the slope of the secant line from x₁ = 0 to x₂ = 4. the slope of the secant line is . (round to the nearest whole number as needed.)

Answer

Explanation:

Step1: Calculate f(0)

Substitute (x = 0) into (f(x)=1.1x^{3}-33x^{2}+260x + 564). [f(0)=1.1\times0^{3}-33\times0^{2}+260\times0 + 564=564]

Step2: Calculate f(4)

Substitute (x = 4) into (f(x)=1.1x^{3}-33x^{2}+260x + 564). [ \begin{align*} f(4)&=1.1\times4^{3}-33\times4^{2}+260\times4 + 564\ &=1.1\times64-33\times16 + 1040+564\ &=70.4-528+1040 + 564\ &=(70.4+1040+564)-528\ &=1674.4-528\ &=1146.4 \end{align*} ]

Step3: Calculate the slope of the secant line

The slope (m) of the secant line between ((x_1,f(x_1))) and ((x_2,f(x_2))) is given by (m=\frac{f(x_2)-f(x_1)}{x_2 - x_1}). Here (x_1 = 0), (x_2=4), (f(x_1)=564), (f(x_2)=1146.4). [m=\frac{f(4)-f(0)}{4 - 0}=\frac{1146.4 - 564}{4}=\frac{582.4}{4}=145.6] Rounding to the nearest whole - number, we get (m = 146).

Answer:

146