Respuesta :
We have an initial value of $9,900.
We have to model the following situations.
a) The value decreases by 11% per year.
We can start expressing this as:
[tex]V(t)=V(t-1)-0.11\cdot V(t-1)=0.89\cdot V(t-1)[/tex]This is a recursive function, as V(t) is function of V(t-1). We can find the explicit function as:
[tex]\begin{gathered} V(t)=0.89\cdot V(t-1) \\ V(t)=0.89(0.89\cdot V(t-1))=0.89^2\cdot V(t-2) \\ \Rightarrow V(t)=0.89^tV(t-t)=0.89^t\cdot V(0) \\ V(t)=9900\cdot0.89^t \end{gathered}[/tex]b) The value decreases by $896 per year
This can be modeled as:
[tex]\begin{gathered} V(t)=V(0)-896\cdot t \\ V(t)=9900-896t \end{gathered}[/tex]c) The value increases by 6% per year
This will have similarities with the function in the point a).
We can model this as:
[tex]\begin{gathered} V(t)=1.06\cdot V(t-1) \\ V(t)=1.06^t\cdot V(0) \\ V(t)=9900\cdot1.06^t \end{gathered}[/tex]d) The value increases by $743 per year
This will be a linear model, as it is the model in point b).
[tex]V(t)=9900+743t[/tex]Answer:
a) V = 9900*0.89^t
b) V = 9900 - 896t
c) V = 9900*1.06^t
d) V = 9900 + 743t
