Question

question 3
consider the following table representing the value of a persons stock portfolio over an eight - month period. using these values, compute the average rate of change of the amount, in dollars per month, over the interval 1,8. round to the nearest dollar per month. do not give any units or labels in your answer, just provide the numerical value.
time (months)\t0\t1\t2\t3\t4\t5\t6\t7\t8
value ($)\t$28,480\t$26,430\t$18,625\t$10,295\t$12,740\t$13,457\t$14,878\t$16,890\t$18,905

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x$ is the number of months and $y$ is the value of the stock portfolio. The initial month $x_1 = 0$ and the final month $x_2=8$. The value at $x = 0$ is $y_1=52840$ and the value at $x = 8$ is $y_2 = 545903$.

Step2: Calculate the average rate of change

The average rate of change $=\frac{y_2 - y_1}{x_2 - x_1}=\frac{545903 - 52840}{8-0}=\frac{493063}{8}=61632.875\approx61633$.

Answer:

61633