s10029564
contestada

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%

Respuesta :

Nonportrit
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!
fenixbm

Answer:

  • The answer is D.

Step-by-step explanation:

If the object starts with a value [tex]V_0[/tex], and a annual percent of decay d, after a year the value will be

[tex]V_1 = V_0 * d[/tex]

after 2 years, taking now  [tex]V_1[/tex] as the starting value

[tex]V_2 = V_1 * d = V_0 * d * d [/tex]

[tex]V_2 = V_0 * d^2 [/tex]

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

[tex]V_n = V_0 * d^n[/tex]

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:

[tex] \$5000 = \$ 9500 * d^{15}[/tex]

Working it a little

[tex] \frac{\$5000}{\$ 9500} = d^{15}[/tex]

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

[tex] (0.5263})^{1/15} = d[/tex]

[tex] 0.9581 = d[/tex]

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

Otras preguntas