Question

1. corporate fraud the number of pending corporate fraud cases stood at 545 at the beginning of 2008 (t = 0) and was 726 at the beginning of 2012. the growth was approximately linear. a. derive an equation of the line passing through the points a(0, 545) and b(4, 726). b. plot the line with the equation found in part (a). c. use the equation found in part (a) to estimate the number of pending corporate fraud cases at the beginning of 2014. source: federal bureau of investigation.

Explanation:

Step1: Calculate slope of the line

The slope $m$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2-y_1}{x_2-x_1}$.
$m = \frac{726 - 545}{4 - 0} = \frac{181}{4} = 45.25$

Step2: Find y-intercept

The y-intercept $b$ is the $y$-value when $t=0$, which is 545.

Step3: Write linear equation

The linear form is $y = mt + b$.
$y = 45.25t + 545$

Step4: Determine t for 2014

2014 is 6 years after 2008, so $t=6$.

Step5: Substitute t=6 into equation

$y = 45.25(6) + 545$
$y = 271.5 + 545 = 816.5$

Answer:

a. $y = 45.25t + 545$
b. (To plot: Mark the points $(0, 545)$ and $(4, 726)$, then draw a straight line passing through them, extending in both directions. The horizontal axis represents $t$ (years after 2008) and the vertical axis represents the number of pending fraud cases.)
c. 817 (rounded to the nearest whole number, or 816.5)