Respuesta :
ANSWER
[tex]\begin{gathered} V(t)=\text{ 28,600\lparen0.986\rparen}^t \\ V(8)\text{ = \$25,548.38} \end{gathered}[/tex]EXPLANATION
Given:
The price of a car in 2010 = $28,600
The cost of depreciation per year = $400
Desired Outcome:
1. V(t)
2. V(8)
Determine the depreciation rate
[tex]\begin{gathered} rate\text{ = }\frac{400}{28600} \\ rate\text{ = 0.013986} \\ rate\text{ = 1.3986\%} \end{gathered}[/tex]Applying the formula for decay
[tex]V\text{ = A\lparen1-r\rparen}^n[/tex]where
A = initial cost price
r = depreciation rate
n = number of years
So the formula for V(t)
[tex]\begin{gathered} V(t)\text{ = 28,600\lparen1 - 0.013986\rparen}^t \\ V(t)\text{ = 28.600\lparen0.986\rparen}^t \end{gathered}[/tex]The value of the in 2018
[tex]\begin{gathered} V(8)\text{ = 28,600\lparen0.986\rparen}^8 \\ V(8)\text{ = 28,600\lparen0.8933\rparen} \\ V(8)\text{ = 25,548.38} \end{gathered}[/tex]Hence, the formula for V(t) is 28,600(0.986)^t and the value of the car in 2018 is $25,548.38
