solve.
1. roller coasters the graph below shows the speed of a roller coaster during the first 30 seconds. describe the change in speed over time.
2. money the graph below shows the amount of money in the soccer club’s account. describe the change in balance over time.
3. hiking the graph below shows the altitude of a hiker during a hike. describe the change in altitude over time.
4. music the graph below shows the tempo of a song as it is played. describe the change in tempo over time.
5. exercise ryan monitored his heart rate while exercising. during the warm up, his heart rate increased slowly. while exercising, his heart rate increased rapidly and then steadied. during cool down, his heart rate lowered quickly. sketch a qualitative graph to represent the situation.

Question

Accepted Answer

### Problem 1: ROLLER COASTERS
# Brief Explanations:
Initially, the speed increases slightly (maybe a slow start). Then there’s a rapid increase (likely a drop or acceleration). After reaching a peak, the speed plateaus briefly, then decreases gradually with small drops (maybe from hills/turns) over the 30 seconds.
# Answer:
- Initial: Slight speed increase.
- Middle: Rapid speed rise, then a plateau, followed by gradual, stepped decreases.
- End: Continues decreasing slowly.

### Problem 2: MONEY
# Brief Explanations:
The balance starts constant (no change). Then it rises (income/ deposit), plateaus (stable period), drops sharply (expense/ withdrawal), then stays constant (no activity).
# Answer:
- Start: Balance is constant.
- Middle: Increases, plateaus, then drops sharply.
- End: Remains constant at a lower level.

### Problem 3: HIKING
# Brief Explanations:
Altitude starts at 0 (start point), increases slowly (gentle climb), then a steeper climb, plateaus (rest/ flat area), drops sharply (descent), then a smaller drop (gentler descent), ending at 0 (back to start).
# Answer:
- Start: Altitude = 0, increases slowly.
- Middle: Steeper climb, plateau, sharp descent, smaller descent.
- End: Returns to 0.

### Problem 4: MUSIC
# Brief Explanations:
Tempo starts constant (steady beat), increases slightly (modest tempo rise), then a steeper increase (faster tempo), plateaus (constant fast tempo), drops sharply (sudden slowdown), then stays constant (back to original tempo).
# Answer:
- Start: Tempo is constant.
- Middle: Slight increase, steeper increase, plateau, sharp drop.
- End: Returns to initial constant tempo.

### Problem 5: EXERCISE (Sketching the Graph)
# Brief Explanations:
- **Warm - up**: Heart rate (y - axis) increases slowly over time (x - axis) → shallow upward slope.
- **Exercising**: Heart rate increases rapidly (steeper upward slope) then steadies (horizontal line).
- **Cool - down**: Heart rate lowers quickly (steep downward slope) to near - resting (ends at a higher but stable rate? Or back to start? Context: After exercise, heart rate stabilizes but not necessarily to 0, but the description says “lowered quickly” – so from the steady exercise rate, drop sharply.

To sketch:
- X - axis: Time; Y - axis: Heart Rate.
- Warm - up: Line with small positive slope.
- Exercise: Steeper positive slope, then horizontal.
- Cool - down: Steep negative slope.

# Answer:
1. **Warm - up Segment**: Shallow upward line (slow increase).
2. **Exercise Segment**: Steep upward line (rapid increase) → horizontal line (steady).
3. **Cool - down Segment**: Steep downward line (quick decrease).

(Graph shape: Three parts – shallow up, steep up + flat, steep down.)

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QUESTION IMAGE

Question

Explanation:

Problem 1: ROLLER COASTERS

Answer:

Problem 2: MONEY