Answer:
[tex]y = 34000(1-0.06) ^ t[/tex]
After 7.40 years it will be worth less than 21500
Step-by-step explanation:
This problem is solved using a compound interest function.
This function has the following formula:
[tex]y = P(1-n) ^ t[/tex]
Where:
P is the initial price = $ 34,000
n is the depreciation rate = 0.06
t is the elapsed time
The equation that models this situation is:
[tex]y = 34000(1-0.06) ^ t[/tex]
Now we want to know after how many years the car is worth less than $ 21500.
Then we do y = $ 21,500. and we clear t.
[tex]21500 = 34000(1-0.06) ^ t\\\\log(21500/34000) = tlog(1-0.06)\\\\t = \frac{log(21500/34000)}{log(1-0.06)}\\\\t = 7.40\ years.[/tex]
After 7.40 years it will be worth less than 21500
