Question

Jeremy bought a new truck for $32,000. The value of the truck after t years can be represented by the formula V = 32,000(.8)^t. When will the truck be worth approximately $6700?
A) in 5 years
B) in 7 years
C) in 8 years
D) in 9 years

Answer 1

$6700=32000(0.8)^t$
divide both sides by 32000
$\frac{67}{320}=0.8^t$
take the ln of both sides
$ln( \frac{67}{320})=ln(0.8^t)$
using the property that $ln(a^b)=b(ln(a))$
$ln( \frac{67}{320})=t(ln(0.8))$
divide both sides by ln(0.8)
$\frac{ln( \frac{67}{320}) }{ln(0.8)} =t$
use calculator
7.00728=t
so in about 7 years


B

Answer 2

Answer:

7 years

Step-by-step explanation: