Question

The 1997 value of an object was $9500. In 2012, it was worth $5000. The annual percent of decay has been constant. What is the annual percent of decay? A) 1.19% B) 2.19% C) 3.19% D) 4.19%

Answer 1

• The answer is D.

Explanation:

If the object starts with a value
`V_0`, and a annual percent of decay d, after a year the value will be

`V_1 = V_0 * d`

after 2 years, taking now
`V_1` as the starting value

`V_2 = V_1 * d = V_0 * d * d`

`V_2 = V_0 * d^2`

and so on, after n years the value will be:

`V_n = V_0 * d^n`

Now, in 1997 the value was $9500, in 2012 the value was $5000. Between 1997 and 2012 there are 15 years, so, our equation will be:

`\$5000 = \$ 9500 * d^(15)`

Working it a little

`(\$5000)/(\$ 9500) = d^(15)`

`((\$5000)/(\$ 9500))^(1/15) = d`

`(0.5263})^(1/15) = d`

`0.9581 = d`

This mean that, after a year, the value will be at 95.81 %, this is, a decay rate of 4.19%.

Answer 2

Hello,

Here is your answer:

The proper answer to this question is option D "4.19%".

Your answer is D.

If you need anymore help feel free to ask me!

Hope this helps!