Question 254425
it depreciates at the rate of 14.3% per year.


this means that the value drops by 14.3% per year.


14.3% / 100% = .143


your equation increased the value by 14.3% per year.


you added .1453*6500 to 6500 to get:


{{{6500 + (6500 * .143)}}}.


when you factor out the 6500, you get:


{{{6500 * (1 + .143)}}} = {{{6500 * 1.143}}}.


that does it for one year.


for n years, you then raised to the exponent of n to get:


{{{6500 * 1.143^n}}}.



your equation should have the decreased the value by 14.3% per year.


you needed to subtract .143*6500 from 6500 to get:


{{{6500 - (6500 * .143)}}}.


when you factor out the 6500, you get:


{{{6500 * (1 - .143)}}} = {{{6500 * .857}}}


that does it for one year.


for n years, you then raised to the exponent of n to get:


{{{6500 * .857^n}}}


where you used x, I used n.   


if you prefer to use x, just replace n with x.


graph of {{{y = 6500 * (1.143)^x}}} looks like this.


the y values of the graph are in hundreds.


6000 = 60
7000 = 70
6500 = 65, etc.


the only x values you are interested are when x is positive.


those values are to the right of the y-axis which is the vertical line when x = 0.


{{{graph (400,400,-1,10,-20,200,65*(1.143)^x)}}}


you can see that as x increases, the value of y increases.


graph of {{{y = 6500 * (.857)^x}}} looks like this.


{{{graph (400,400,-1,10,-20,200,65*(.857)^x)}}}


you can see that as x increases, the value of y decreases.