Question

The 2006 value of a car was $18,000. In 2016, it was worth $4000. If the annual percent of decay has been constant, what is the annual percent of decay?

Answer 1

Answer:

$13.96\%$  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

$V=P(1-r)^{x}$  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

$P=\ 18,000\\r=?\\x=10\ years\\V=\ 4,000$

substitute in the formula

$\ 4,000=\ 18,000(1-r)^{10}$  

Simplify

$(2/9)=(1-r)^{10}$  

$(2/9)^{1/10}=(1-r)$  

$r=1-(2/9)^{1/10}$  

$r=0.1396$  

convert to percent

$r=0.1396*100=13.96\%$