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?

Answer 1

Well you would do 0.8^2 and then times that by 32,000
Which would equal 20480

Answer 2

Answer: 7 years

Step-by-step explanation:

Given: The initial price of truck = $32,000

The value of the truck after t years can be represented by the formula ,

$V=32,000(0.8)^t$

To find the time t in years after which the worth of the truck will be approximately $6700, we need to substitute V=6700 in the equation, we get

$6700=32,000(0.8)^t\\\\\Rightarrow(0.8)^t=\frac{6700}{32000}\\\\\Rightarrow(0.8)^t=0.209375$

Taking log on both sides, we get

$t\log(0.8)=\log(0.209375)\\\\\Rightarrow t=\frac{\log(0.209375)}{\log(0.8)}\\\\\Rightarrow t=7.00727566266\approx7$

Hence, after 7 years the worth of the truck will be approximately $6700.