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%

The annual depreciation rate is 72.86%.

Step-by-step explanation:

The information provided are:

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:

Here,

y = final value

a = initial value

r = rate of depreciation

x = time

Compute the annual depreciation rate as follows:

Thus, the annual depreciation rate is 72.86%.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584