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