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For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year. The value, V(t) of $393,000 worth of assets after t years, that depreciate at 15% per year, is given by the formula V(t) = Vo(b)t. What is the value of Vo and b, and when rounded to the nearest cent, what are the assets valued at after 7 years?

Respuesta :

Aliwohaish12
Hi there
The formula is
V (t)=vo (b)^t
V (t) future value?
Vo present value 393000
B=1-0.15= 0.85
T time 7 years

V (7)=393,000×(0.85)^(7)=125,986.8
Round your answer to b 125987

Hope it helps
JeanaShupp

Answer: $ 125987.80

Step-by-step explanation:

Given: The value, V(t) of $393,000 worth of assets after t years, that depreciate at 15% per year, is given by the formula

[tex]V (t)=V_o(b)^t[/tex], here [tex]V_o[/tex] is the initial asset value  and b is the multiplicative decay factor.

The exponential decay function is given by ;-

[tex]f(x)=A(b)^x[/tex], where A is the initial value , x is the  times period and b is the multiplicative decay factor.

where b = 1-r, r is the rate of decay.

Since r = 15%=0.15

Therefore, b = 1-0.15=0.85

Now ,for 7 years , the value of assets is given by :-

[tex]V=393000(0.85)^7=125986.795\approx125987.80[/tex]

Hence, the assets valued at after 7 years = $ 125987.80