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

7 years

Explanation:

Answer 2

`6700=32000(0.8)^t`
divide both sides by 32000

`(67)/(320)=0.8^t`
take the ln of both sides

`ln( (67)/(320))=ln(0.8^t)`
using the property that
`ln(a^b)=b(ln(a))`

`ln( (67)/(320))=t(ln(0.8))`
divide both sides by ln(0.8)

`(ln( (67)/(320)) )/(ln(0.8)) =t`
use calculator
7.00728=t
so in about 7 years


B