V =$27500 Initial Value
V= 2292
1) Considering that equation
The initial value for that car is when it is brand new. At instant t=0, no depreciation so:
[tex]\begin{gathered} V(t)=27500(0.78)^t \\ \text{The initial value:} \\ V(0)=27500(0.78)^0\Rightarrow V(0)\text{ =27500} \end{gathered}[/tex]As the property of exponents says that any number raised to zero, is equal to 1 then the car is worth V =$27500
b) The value after 10 years. Now after 10 yrs of devaluating that car:
[tex]\begin{gathered} V(t)=27500(0.78)^t \\ V(10)=27500(0.78)^{10} \\ V(10)\text{ =2292.33} \\ V(10)\cong2292 \end{gathered}[/tex]All we have to do is to plug it into t the value of 10. After 10 years that
car is worth approximately $ 2292
