Step 1 — Translate the 20% decline per year into a multiplier: A 20% decline means each year the motorcycle keeps 80% of its value. The yearly multiplier is 1 - 0.20 = 0.80.
Step 2 — Write the exponential model: With initial value V(0) = 20,000 dollars and multiplier 0.8 per year, the value after t years is
V(t) = 20000(0.8)^t
Step 3 — Interpret and give sample points:
- At t = 0: V(0) = 20,000 (the y-intercept).
- At t = 1: V(1) = 20000(0.8) = 16,000.
- At t = 2: V(2) = 20000(0.8)^2 = 12,800.
Step 4 — Describe the graph: The graph is an exponential decay curve that starts at (0, 20000) and decreases toward 0 as t increases. It is always positive and has a horizontal asymptote y = 0. If you are modeling only whole years, plot the points above for integer t; if you allow real t, the continuous curve V(t) = 20000(0.8)^t is appropriate.
Conclusion — Which graph models V(t)? The correct graph is the exponential decay curve that starts at 20,000 when t = 0, falls to 16,000 at t = 1, and continues decreasing toward 0 with base 0.8: V(t) = 20000(0.8)^t.