Question

Please help!!! Algebra

Answer 1

Answer:

(2) it decreases by 22% per year

Step-by-step explanation:

The value of the portfolio is described by the expression

$v(x)=30,000 (0.78)^x$

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:

$v(1)=30,000(0.78)^1=23,400$

So, the loss in value of the portfolio in one year is:

$\Delta v = v(1)-v(0)=23,400-30,000=-6,600$

And so, the loss percentage in the portfolio is:

$\frac{\Delta v}{v(0)}\cdot 100 = \frac{-6,600}{30,000}\cdot 100 =-22\%$

So the correct answer is

(2) it decreases by 22% per year