At the band's peak of popularity, a personally signed Black Diamond poster sold for $500. Three years later the band was almost

Question

levacccp

1 month ago

8

At the band's peak of popularity, a personally signed Black Diamond poster sold for $500. Three years later the band was almost

forgotten and the poster was worth only $10. What were the annual multiplier and annual percent of decrease?

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-02-19T21:55:00+03:00

Response:

The yearly multiplier stands at 0.27, while the percentage decrease annually is 73%.

Detailed explanation:

Given the following:

Initial Value $a_i = \$500$

Elapsed time $n= 3\ years$

Final Value $a_3 = \$10$

We aim to determine both the annual multiplier and the yearly percent decrease.

Calculation:

We understand that;

The final amount after a certain number of years is computed by multiplying the initial amount with the multiplier raised to the number of years that have passed.

In equation form, it is represented as;

$a_n=a_i\times (m)^n$

m ⇒ annual multiplier

Plugging in the values results in;

$10=500\times (m)^3\\\\m^3=\frac{10}{500}\\\\m^3=\frac{1}{50}$

By taking the cube root, we find;

$\sqrt[3]{m^3}=\sqrt[3]{\frac{1}{50}} \\\\m=0.27$

Thus, the annual multiplier calculates to 0.27.

Now we will ascertain the annual percent decrease.

We know that;

The annual multiplier equals one minus the rate of depreciation.

$m=1-r$

r ⇒ annual percent decrease.

$0.27 =1-r\\\\r = 0.73\ \ Or \ \ 73\%$

Consequently, the Annual Percent in decrease is 73%.