| Time (min) | Motor power % | Change from last |
|---|---|---|
| 0 | 100% | — |
| 1 | 79% | −21% |
| 2 | 58% | −21% |
| 3 | 37% | −21% |
↑ This is your data. You're looking for the rule that produces it.
Use the data below. What's actually going on?
| Time (min) | Motor power % | Change from last |
|---|---|---|
| 0 | 100% | — |
| 1 | 79% | −21% |
| 2 | 58% | −21% |
| 3 | 37% | −21% |
| 4 | 20% | −17% (?) |
| 5 | 20% | 0% |
What do you notice about how the power changes? Write what you see. Use at least one number from the table in your answer.
Before you see what the formula produces — commit to an answer.
| Time (min) | Motor power % | Change |
|---|---|---|
| 0 | 100% | — |
| 1 | 79% | −21% |
| 2 | 58% | −21% |
| 3 | 37% | −21% |
| 4 | 20% | −17% (?) |
| 5 | 20% | 0% |
Looking at the data above — will Bot #14's battery power ever reach 0%?
Power didn't drain to zero. Describe the rule — in two parts.
| Time (min) | Motor power % | Change |
|---|---|---|
| 0 | 100% | — |
| 1 | 79% | −21% |
| 2 | 58% | −21% |
| 3 | 37% | −21% |
| 4 | 20% | −17% (?) |
| 5 | 20% | 0% |
You've described the pattern. Now what kind of math captures it?
Look at what you've observed: a steady drop, then a flat stop. What math does that?
Every bot loses power as the match wears on — unless your Endurance stat is high enough to slow the drain. This formula shows exactly how much power your bot has at any minute of a match.
| Variable | Meaning | Range |
|---|---|---|
| P(t) | Bot power at minute t (% of full power) | 20% – 100% |
| E | Endurance allocation — stat points invested in stamina | 1 – 20 |
| t | Minutes elapsed since match start | 0 – 5 min |
| 1.5 | Decay constant — how fast the game environment drains power | fixed |
⚡ If the formula gives less than 20%, power is capped at 20% — that's the power floor.
Fill in the missing values. Use the formula: P(t) = 100 − (20 − E) × 1.5 × t
With E = 4, the decay rate is (20 − 4) × 1.5 = 24% per minute. Fill in the product (24 × t) and then P(t) for each row. Submit each row when ready.
| t | 24 × t = ? | P(t) = 100 − ? |
|---|
Now on your own. With E = 2, calculate the full product (decay × t) and P(t) for each minute. No hints this time.
| t | Full product | P(t) |
|---|
Move the slider. Figure out what E controls.
Change E. What changes? What stays the same?
Find an E value so the battery is still above 60% at t = 3.
Use the graph. Test values. When you find one that works, enter it below.
Show what you figured out — in math.
| Time (min) | Motor power % | Change |
|---|---|---|
| 0 | 100% | — |
| 1 | 79% | −21% |
| 2 | 58% | −21% |
| 3 | 37% | −21% |
| 4 | 20% | −17% (?) |
| 5 | 20% | 0% |
Formula: P(t) = 100 − (20 − E) × 1.5 × t · floor at 20% · E = 6 for Bot #14
Write a rule for power over time using math. Include when the behavior changes.
Tap a starter to add it:
Connect your E to the match. Then commit.
Answer all three questions. Use the sentence frames as a starting point, then make it your own.
1. What happens to your bot's power during the match?
2. How does your E compare to a teammate running E=8?
3. Why does your E choice make sense for the match?
Record this on your individual stat card before you leave the table.