Question

Milton has his money invested in a stock portfolio. The value, v(.r), of his

portfolio can be modeled with the function y(x) = 30,000(0.78)", where x is the
number of years since he made his investment. Which statement describes the rate
of change of the value of his portfolio?
A) It decreases 78% per year. B) It decreases 22% per year.
C) It increases 78% per year. D) It increases 22% per year.​

Answer 1

B) It decreases 22% per year.

Explanation:

We are given that The value, v(.r), of his portfolio can be modeled with the function :
`y(x) = 30,000(0.78)^x`

Where x is the number of years since he made his investment.

Formula :
`P(1-r)^t=A`

Where P = Principal

r = rate of decrease

t = time

A = Amount after t years

So, On comparing

P = 30000

t=x

A=y(x)

`1-r=0.78`

`\Rightarrow 1-0.78=r`

`\Rightarrow 0.22=r`

So, r = 0.22

r=22%

So, Rate of decrease is 22%

So, Option B is true,

It decreases 22% per year.