Question

question 9 consider the following data representing the value of a persons stock portfolio over an eight - month period. using mean values, compute the average rate of change of their account, 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 include the numerical value.
time (months) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
value ($) | 105,990 | 106,200 | 106,985 | 97,893 | 96,790 | 92,554 | 90,475 | 102,880 | 103,303

Explanation:

Step1: Recall the formula for the average rate of change

The average rate of change of a function \( f(t) \) over the interval \([a, b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \( a = 0 \) (time in months) and \( b=8 \) (time in months), \( f(t) \) is the value of the portfolio at time \( t \). So we need to find \( f(8) \) and \( f(0) \) from the table.
From the table, when \( t = 0 \), \( f(0)=105000 \) and when \( t = 8 \), \( f(8)=123000 \).

Step2: Calculate the average rate of change

Using the formula \(\frac{f(8)-f(0)}{8 - 0}\), substitute the values:
\(\frac{123000 - 105000}{8-0}=\frac{18000}{8}\)
Simplify the fraction: \(\frac{18000}{8}=2250\)

Answer:

2250