Question

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.
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.)

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