Answer:
The value of car after T years of sold is $5,000 [tex](0.9)^{\textrm T}[/tex]
Step-by-step explanation:
The initial value of car = i = $5,000
The value of car decreases every years at rate = r = [tex]\dfrac{1}{10}[/tex] = 0.1 = 10%
Let The value of car after T years of sold = $f
Now, According to question
The value of car after T years of sold = initial value of car × [tex](1-\frac{rate}{100})^{\textrm time}[/tex]
I.e f = i × [tex](1-\frac{r}{100})^{\textrm T}[/tex]
Or, f = $5,000 × [tex](1-\frac{10}{100})^{\textrm T}[/tex]
Or, f = $5,000 × [tex](0.9)^{\textrm T}[/tex]
So,The value of car after T years = f = $5,000 [tex](0.9)^{\textrm T}[/tex]
Hence,The value of car after T years of sold is $5,000 [tex](0.9)^{\textrm T}[/tex] Answer
