Compute $V(1)$ and compare it to $V(0)$. How do you get from $V(0)$ to $V(1)$ using multiplication?

Rewrite $0.8$ as a percentage. Does that percentage represent how much is kept each year or how much is lost each year?

Based on how the value changes from year to year in the formula, which option describes that multiplicative change (not an addition or subtraction of a fixed dollar amount)?

Type V(d)=12000*(0.8)^d into Desmos. If Desmos uses x by default, you can instead type y=12000*(0.8)^x.

Create a table for the function and include the row where $d=0$ (or $x=0$). Observe the value of $V(0)$ to see the motorcycle’s price when it was purchased.

In the same table, look at the values for consecutive integers, such as $d=0$ and $d=1$, then $d=1$ and $d=2$. Compare each new value to the previous one (for example, divide $V(1)$ by $V(0)$). Notice the factor you are multiplying by each year and think about what that factor represents as a percentage.

The model is

This has the form $V(d) = a \times b^d$, where:

• $a$ is the initial value when $d=0$.
• $b$ is the growth or decay factor per time period (here, per year).

To see the initial value, plug in $d=0$:

So the motorcycle was worth $12,000 when it was purchased, not $0.80 and not something involving $8,000.

Now look at what happens as $d$ increases by 1:

• $V(1) = 12{,}000(0.8)^1 = 12{,}000 \times 0.8$.
• $V(2) = 12{,}000(0.8)^2 = 12{,}000 \times 0.8 \times 0.8$.

Each time you increase $d$ by 1 (one more year), the value is multiplied by $0.8$ again. So $0.8$ tells you how much of the previous year’s value the motorcycle keeps each year.

The number $0.8$ is the same as $80\%$. So each year, the motorcycle keeps $80\%$ of its value from the previous year, which means it loses the other $20\%$ each year.

Therefore, the correct interpretation is: “Each year, the motorcycle keeps 80% of its value from the previous year, a 20% decrease per year.” (choice D).