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

Answer:

• The answer is D.

Step-by-step 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

$\frac{\ 5000}{\ 9500} = d^{15}$

$(\frac{\ 5000}{\ 9500})^{1/15} = d$

$(0.5263})^{1/15} = d$

$0.9581 = d$

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!