Respuesta :
32,300 / 8.3 = x , how much value it loses monthly.
x = $3891.56627
x = $3891.56627
Calvin purchases a piece of heavy machinery for $32,300. The value of the machine depreciates at an annual rate of 8.3%
Annual depreciation rate = 8.3% = [tex] \frac{83}{100} = 0.083 [/tex]
For monthly depreciation rate we we raise to the exponent [tex] \frac{1}{12} [/tex]. Also we multiply the number of years by 12.
We know depreciation formula is
[tex] A = p (1 - r)^t [/tex]
Where 'p' is the initial cost, 'r' is the annual depreciation rate and 't' is the number of years
Here p = 32,300
r = 0.083 for monthly we raise to the exponent [tex] \frac{1}{12} [/tex]
so [tex] (1-r)\frac{1}{12}^ [/tex]
t= number for years , for monthly we put 12t
So equation becomes
[tex] A = 32300 ( (1-0.083)^\frac{1}{12} )^{12t} [/tex]
[tex] A = 32300 ( 0.917^\frac{1}{12} )^{12t} [/tex]
function of represents the value of the machine with an approximate equivalent monthly depreciation rate is
[tex] f(t) = 32300 ( 0.917^\frac{1}{12} )^{12t} [/tex]
