A car has an initial value of $20,000. The value then "depreciates" or decreases by 10% of its initial value each year. Which equation below gives the value of the car, v, after y years?

a. v = - 0.10y + 2,000
b. v = 0.10y - 2,000
c. v = 2,000y - 20,000
d. v = -2,000y + 20,000

Question

A car has an initial value of $20,000. The value then "depreciates" or decreases by 10% of its initial value each year. Which equation below gives the value of the car, v, after y years?

a. v = - 0.10y + 2,000
b. v = 0.10y - 2,000
c. v = 2,000y - 20,000
d. v = -2,000y + 20,000

mathstudent55 · Answer

The car's original value is y.
After 1 year, it lost 10% of its value.
How much value did it lose in 1 year?

madeleine2 · Answer

is the answer b?

mathstudent55 · Answer

No.

mathstudent55 · Answer

If the car is worth y, and it loses 10% of its value in 1 year, how mucgh value in terms of y does it lose in 1 year?

madeleine2 · Answer

is it neither a or b becuase y is supposed to be 20,000 or is it the other way around

madeleine2 · Answer

wait is the answer then c

mathstudent55 · Answer

Are you going to guess the answers one by one until you get tot he correct one?
I think it's better to understand it and figure out the correct answer without guesses.

mathstudent55 · Answer

The car was worth $20,000 to start with.
It loses in value 10% of $20,000 each year.
How much does it lose in value each year?
In other words, what is 10% of $20,000?

madeleine2 · Answer

no i think its c becuase its subracting which means its decreasing

mathstudent55 · Answer

I see a negative sign in both c and d.
How can you tell it's c and not d?
Please answer my question above. We'll get to the correct answer soon.

mathstudent55 · Answer

Can you answer this?

The car was worth $20,000 to start with.
It loses in value 10% of $20,000 each year.
How much does it lose in value each year?
In other words, what is 10% of $20,000?

madeleine2 · Answer

10% of $20,000 is 2000

mathstudent55 · Answer

Correct.
The car started with a value of $20,000.
Each year that goes by, it loses another $2,000 in value.
Ok so far?

mathstudent55 · Answer

Year 0 value: 20,000
Year 1 value: 20,000 - 2000
Year 2 value: 20,000 - 2000 - 2000 = 20,000 - 2000(2)
Year 3 value: 20,000 - 2000 - 2000 - 2000 = 20,000 - 2000(3)
Year 4 value: 20,000 - 2000 - 2000 - 2000 - 2000 = 20,000 - 2000(4)
etc.
Year y value: 20,000 - 2000y

mathstudent55 · Answer

Each year it loses $2000.

In the first year it loses $2000 in value.

In the second year it has lost 2-years' worth of $2000 a year loss, so it already lost 2 * $2000 = $4000.

In the third year, it has had 3 years of losing $2000 per year, so at eh end of the 3rd year, it has lost 3 * $2000 in value.

For each year that passes, multiply the number of years by $2000, and subtract from the original value of $20,000.

In year y, it has lost 2000y in value.
Since it started at a value of 20,000, in year y it is worth
20,000 - 2000y.

20,000 - 2000y is the same as -2000y + 20,000