The value of an industrial machine has a decay factor of 0.75 per year. After six years, the machine is worth 7500. What was the original value of the machine?

1 Answer
Jul 21, 2016

I found: #30,720,000# BUT I used a cumulative effect impacting #0.75# upon the reduced values of each year.

Explanation:

Call the original value #x#;
after the first year the value will become:
#x-0.75x#
after the second year:
#(x-0.75x)-0.75(x-0.75x)=(x-0.75x)(1-0.75)#
after the third year:
#[(x-0.75x)(1-0.75)]-0.75[(x-0.75x)(1-0.75)]=(x-0.75x)(1-0.75)(1-0.75)=(x-0.75x)(1-0.75)^2#
so basically we have that after the nth year:

#(x-0.75x)(1-0.75)^(n-1)#

in 6 years:
#(x-0.75x)(1-0.75)^5=7500#
#0.25x=7500/(1-0.75)^5#
so:
#x=30,720,000#