v=12000e(^-0.6t) t=years v=$ a)what is price after 3 years? b) find nearest month when price is halfed?

Question

they are talking about a car depreciating. the purcase price of the car is $12000
the actual answers are
a)1983.57
b)14 months

Answer 1

V=12000e(^-0.6t) t=years v=$
a)what is price after 3 years?
V(3) = 12000e(^-0.6(3))
b) find nearest month when price is halfed?
12000e(^-0.6t) = 6000
e^{-0.6t} = 1/2
-0.6t = ln( 1/2)
t = ln(1/2) / (-0.6)
they are talking about a car depreciating. the purcase price of the car is $12000
the actual answers are
a)1983.57
b)14 months

Answer 2

v=12000e(^-0.6t)
v = 12000e^-1.8 =12,000 * .165298882 = $1983.59

6000 =12000 e^-.6t
.5 = e^-.6t
ln(.5) = -.6t
t = ln(.5)/-.6 = 1.155 years = 13.86 months = 14 months