Question

12. Suppose you buy a car in 2018 for $15200. If your car depreciate at a rate of 14.5% per year, how long will it take for your to reach half of its worth?

Answer 1

depreciate rate is 14.5%

r=0.145

.

b=1-r

b=1-0.145

b=0.855

.

initial amount = a

.

equation is

$y=a\cdot b^t$

$y=a\cdot (0.855)^t$

for half life take   $y=\frac{a}{2}$

$\frac{a}{2}=a(0.855)^t$

$\frac{1}{2}=(0.855)^t$

$0.5=(0.855)^t$

$\ln(0.5)=t\ln(0.855)$

$t=\frac{\ln(0.5)}{\ln(0.855) }$

$t=\frac{-0.69315 }{-0.15665 }$

$t=4.42471$

.

it takes 4.425 years to reach half of its worth