the function f(x)=1.2x³ - 32x² + 266x + 553 models the number of discharges from the military, f(x), of…

the function f(x)=1.2x³ - 32x² + 266x + 553 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.\na. find the slope of the secant line from x1 = 0 to x2 = 4.\nthe slope of the secant line is \n(round to the nearest whole number as needed.)

the function f(x)=1.2x³ - 32x² + 266x + 553 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.\na. find the slope of the secant line from x1 = 0 to x2 = 4.\nthe slope of the secant line is \n(round to the nearest whole number as needed.)

Answer

Explanation:

Step1: Recall slope - formula for secant line

The slope of the secant line between two points ((x_1,y_1)) and ((x_2,y_2)) on the graph of (y = f(x)) is given by (m=\frac{f(x_2)-f(x_1)}{x_2 - x_1}). Here, (x_1 = 0), (x_2=4), and (f(x)=1.2x^{3}-32x^{2}+266x + 553).

Step2: Calculate (f(x_1))

When (x_1 = 0), (f(0)=1.2\times0^{3}-32\times0^{2}+266\times0 + 553=553).

Step3: Calculate (f(x_2))

When (x_2 = 4), (f(4)=1.2\times4^{3}-32\times4^{2}+266\times4 + 553). First, (1.2\times4^{3}=1.2\times64 = 76.8). Second, (32\times4^{2}=32\times16 = 512). Third, (266\times4=1064). Then (f(4)=76.8-512 + 1064+553=1181.8).

Step4: Calculate the slope

(m=\frac{f(4)-f(0)}{4 - 0}=\frac{1181.8 - 553}{4}=\frac{628.8}{4}=157.2\approx157).

Answer:

157