Is the change described as a fixed dollar amount each year, or as a fixed percentage each year?

Linear models use the same added or subtracted amount each year, while another common model type uses the same multiplying factor (like a constant percent change). Decide which one matches the situation here.

Once you decide whether the value is going up or down, and whether it changes by a constant amount or a constant percentage, choose the option that matches both of those features.

Because the laptop keeps 80% of its value each year (after a 20% loss), type into Desmos: y = 1200*(0.8)^x, where x is the number of years since purchase and y is the resale value.

Look at the graph of y = 1200*(0.8)^x. Notice whether it goes up or down as x increases, and whether it is a straight line or a curve that bends and flattens out over time. Then, among the choices, pick the description that matches a graph that behaves like this.

The laptop is bought for $1. Each year, its resale value decreases by 20 percent, which means each year it keeps 80 percent (because $100\% - 20\% = 80\%$) of its value from the previous year.

If $V$ is the value and $t$ is the number of years since purchase:

• At $t=0$: $V = 1200$.
• After 1 year: $V = 1200 \times 0.8$.
• After 2 years: $V = 1200 \times 0.8 \times 0.8 = 1200 \times 0.8^2$.
• After 3 years: $V = 1200 \times 0.8^3$.

In general, the pattern is $V(t) = 1200 \times 0.8^t$.

The factor $0.8$ is less than $1$, so each year you multiply by a number smaller than $1$. That makes the value go down over time, so the function is decreasing, not increasing.

A linear function changes by adding or subtracting the same fixed amount each year (for example, always losing $1 each year). Here, the laptop loses the same percentage each year, which means it is multiplied by the same factor $0.8$ each year. A repeated multiplication by a constant factor is an exponential relationship. Because the function is both decreasing and exponential, the best model is a decreasing exponential function.