Respuesta :
Answer:
The original price of the car = $20,625
It will take 11 years or this car to fully straight line depreciate.
Step-by-step explanation:
Given:
The straight line depreciation of a car is given as:
[tex]y=-1,875x+20,625[/tex]
To find the original price of the car and the number of years it takes for this car to fully straight line depreciate.
Solution:
The straight line depreciation equation is given as:
[tex]y=-mx+b[/tex]
where [tex]m[/tex] represents the rate of depreciation per year, [tex]x[/tex] represents number of years and [tex]b[/tex] represents the original value.
From the given equation we can see that the original value [tex]b[/tex] is = 20,625
Thus, the original price of the car = $20,625
To find he number of years it takes for this car to fully straight line depreciate, we will substitute [tex]y=0[/tex] as the value of car is fully depreciated.
So, we have:
[tex]0=-1,875x+20,625[/tex]
We can now solve for [tex]x[/tex] to get the number of years it takes for this car to fully straight line depreciate.
Adding [tex]1,875x[/tex] both sides.
[tex]0+1,875x=-1.875x+1,875x+20,625[/tex]
[tex]1,875x=20,625[/tex]
Dividing both sides by 1,875
[tex]\frac{1,875x}{1,875}=\frac{20,625}{1,875}[/tex]
∴ [tex]x=11[/tex]
Thus, it will take 11 years or this car to fully straight line depreciate.
