Question

. A certain vehicle loses 35% of its value each year.18. If the vehicle has an initial value of $25,000, construct a model that represents the value after t years.19. Compute the value of the vehicle at the end of the 3rd year. (round to the hundredths place)

Answer 1

18.

To model this situation, we can use an exponential equation:

$y=a\cdot(1+r)^t$

Where a is the initial value, t is the time in years and r is the rate of increase or decrease.

So for this case, we have a = 25000 and r = -0.35 (negative because the value decreases each year).

Therefore the equation is:

$\begin{gathered} y=25000\cdot(1-0.35)^t \\ y=25000(0.65)^t \end{gathered}$

19.

After 3 years (that is, for t = 3), the price of the vehicle will be:

$\begin{gathered} y=25000(0.65)^3 \\ y=25000\cdot0.274625 \\ y=6865.62 \end{gathered}$

The price will be $6,865.62.