Question

PLZ HELP!!!
At the band’s peak of popularity, a signed Black Diamond poster sold for $500. Three years later, the band was almost forgotten, and the poster was worth only $10. Write a function that will allow you to calculate how much the poster is worth after x years. State the meaning of each part of the equation in the context of the problem.

The annual depreciation rate is 72.86%

Answer 1

Answer:

The annual depreciation rate is 72.86%.

Step-by-step explanation:

The information provided are:

• At the band’s peak of popularity, a signed Black Diamond poster sold for $500.
• Three years later, the band was almost forgotten, and the poster was worth only $10.

From the above data we know that the band's popularity depreciated.

The initial cost of a signed Black Diamond poster was, a = $500.

After three years the cost of a signed Black Diamond poster was, y = $10.

It can be seen that the value of a signed Black Diamond poster is decreasing exponentially over the years.

The formula for exponential decay or depreciation is:

$y=a(1-r)^{x}$

Here,

y = final value

a = initial value

r = rate of depreciation

x = time

Compute the annual depreciation rate as follows:

         $y=a(1-r)^{x}$

        $10=500\times (1 -r)^{3}$

$(1-r)^{3}=\frac{10}{500}$

 $(1-r)=\sqrt[3]{\frac{1}{50}}$

    $1-r=0.2714$

          $r=1-0.2714\\\\r=0.7286$

Thus, the annual depreciation rate is 72.86%.