I don't get this kind of math question.?

Question

each year, the value of a car depreciates to 70% of its value the previous year. A car was bought new for $25000. Determine its approximate value at the end of every year, for 5 years

Answer 1

Value(Years) = (Depreciation ^ Years) * Original_Value

Value(1) = (0.7 ^ 1) * $25,000 = $17,500
Value(2) = (0.7 ^ 2) * $25,000 = $12,250
Value(3) = (0.7 ^ 3) * $25,000 = $8,575
Value(4) = (0.7 ^ 4) * $25,000 = $6,002.50
Value(5) = (0.7 ^ 5) * $25,000 = $4,201.75

You might ask, "how did you get that equations kookie?" That's simple enough.

D = Depreciation
V0 = Original Value

V1 = D * V0
V2 = D * V1
V3 = D * V2
V4 = D * V3
V5 = D * V4

If you expand V5, you get this equation.
V5 = D * (D * (D * (D * ( D * V0))))

If you simplify that equation, you get this equation.
V5 = (D ^ 5) * V0

It's easy enough to see that you can make a general equation for any number of years.

Answer 2

$4,201.75

Just take 70% of the previous year's value after each year.

After the first year: 25,000 x 0.7 = 17,500

After the 2nd year: 12,250

After the 3rd year: 8,575

After the 4th year: 6,002.50

After the 5th year: 4,201.75

Note that the dollar amount of depreciation gets smaller every year, even though the percentage stays the same. Calculating 70% of a number is the same as multiplying by 70/100 or 7/10 or 0.7. Or you can reach the same conclusion, but with more work, by subtracting 30% each year.

Answer 3

year 1 - 25000 x .70= 17500
year 2 - 17500 x .70 = 12250
year 3 - 12250 x .70 = 8575
year 4 - 8575 x .70 = 6002.50
etc

Answer 4

It is basic multiplication. Every year, the car is worth 70% of it's then current value. So:

year 1 : 17500 (25000 * 0.70)
year 2 : 12250 (17500 * 0.70)
year 3 : 8575 (12250 * 0.70)
year 4 : 6002.50 (8575 * 0.70)
year 5 : 4201.75 (6002.50 * 0.70)

Answer 5

25000 - 70% = yr1
yr1 - 70% = yr2
yr2 - 70% = yr3 and so on and so forth