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

Answer: After 7 years the truck will be worth of $6700.

Explanation:

Since we have given that

Value of a new truck that Jeremy bought = $32000

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

`V=32000(0.8)^t\\`

We need to find the number of years after which the worth of truck will be $6700.

According to question,

`6700=32000(0.8)^t\\\\(6700)/(32000)=0.8^t\\\\0.21=0.8^t\\\\\text{ Taking Logarithm on both the sides}\\\\\log(0.21)=t\log(0.8)\\\\(\log(0.21))/(\log(0.80)=t\\\\6.99=t\\\\7\ years=t`

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

Answer 2

The truck Jeremy bought new was $32,000. The value of the truck after T years can be represented by the formula V=32,000 (.8)T. The truck will be worth approximately $6,700 in 8 years.