Answer:
The value at the end of the fifth year (a5) is equal to $5,696.
As the number of years n is the exponent of a number that is smaller than 1, the value of the car is decreasing with the years.
We also can conclude that the value of the car decreases 25% each year.
Step-by-step explanation:
The value of the car is represented by an=24000(3/4)^n, where n is the year.
The value at the end of the fifth year (a5) is equal to:
[tex]a_5=24,000\left(\dfrac{3}{4}\right)^5=24,000*0.2373=5,695[/tex]
As the number of years n is the exponent of a number that is smaller than 1, the value of the car is decreasing with the years.
We also can conclude that the value of the car decreases 25% each year:
[tex]a_n/a_{n-1}=(3/4)^{n-(n-1)}=(3/4)^1=0.75[/tex]
