Answer:
(2) it decreases by 22% per year
Step-by-step explanation:
The value of the portfolio is described by the expression
[tex]v(x)=30,000 (0.78)^x[/tex]
where
30,000 is the value of the initial portfolio
x is the number of years
0.78 is the rate of change of the portfolio
To answer the question, we evaluate the value of the portfolio after one year, that is when
x = 1
Substituting into v(x), we find:
[tex]v(1)=30,000(0.78)^1=23,400[/tex]
So, the loss in value of the portfolio in one year is:
[tex]\Delta v = v(1)-v(0)=23,400-30,000=-6,600[/tex]
And so, the loss percentage in the portfolio is:
[tex]\frac{\Delta v}{v(0)}\cdot 100 = \frac{-6,600}{30,000}\cdot 100 =-22\%[/tex]
So the correct answer is
(2) it decreases by 22% per year
