A new automobile is purchased for $20,000. If V = 20,000(0.8)^x give s the car's value after x years, then ABOUT how long will it take for the car to be worth half its purchase price? a) 3 years b) 4 years c) 5 years d) 6 years

Question

anonymous · Answer

substitute v = 10000 in the equation and solve for x.
alternatively, plug in x =3,4,5,6 and see which one yields 10000

anonymous · Answer

$$V=10000=20000\times0.8^x \implies0.8^x=\frac{10000}{20000}=0.5\implies x=\log_{0.8}0.5\approx3$$So 3 years.

anonymous · Answer

did that and got A, but it says half its original price and 10,240 isnt quite half yet. so i wasnt sure
Thanks guys