Answer:
Cost of the tires in 2008 = 23333 dollars
Step-by-step explanation:
Number of snow tires purchased are represented by,
T = [tex]\frac{500(t+20)}{(t+75)}[/tex]
Where t = duration from year 2000
Similarly, cost of the tires area represented by,
C = [tex]\frac{t+75}{1-.05t}[/tex]
Therefore, cost of T tires = C × T
= [tex]\frac{t+75}{1-.05t}[/tex] × [tex]\frac{500(t+20)}{(t+75)}[/tex]
= [tex]\frac{500(t+20)}{1-0.05t}[/tex]
Now cost of the tires in year 2008 (t = 8 years)
Total cost = [tex]\frac{500(8+20)}{(1-0.05\times 8)}[/tex]
= [tex]\frac{14000}{0.6}[/tex]
= $23333.3
≈ 23333 dollars