Separate processes with different percent changes and a stated total change call for two equations about their original amounts. Those equations form a system of equations: graph both in Desmos and click their intersection. Use percent multipliers, numbers that turn an old amount into a new one, for each year. A later year's percent acts on the preceding year's amount.
Hints
- Hint 1
A percent multiplier describes the whole new amount: a increase means of the original, while a decrease leaves . If and are the 2023 amounts, what are the two 2024 amounts?
- Hint 2
The total increased by , so the 2024 sum is of the entire 2023 sum, not of either process alone. Equate that to the sum of the two separately changed amounts.
- Hint 3
A successive percent change starts from the previous year's amount. Write the 2025 amount for each process using its 2024 amount, then add them and match the given total. You'll have two equations to graph together.
Step-by-step
Model each year, then graph the system
Step 1Write each process's 2024 amount
Let and be the 2023 amounts for Process A and Process B, in megawatt-hours. A percent multiplier turns an old amount into a new one. A's increase makes its 2024 amount . B's decrease leaves its 2024 amount at .
- Step 2
Use the change in the total
The 2023 total is , so a increase makes the whole 2024 total . That must equal the sum of the two 2024 process amounts: .
- Step 3
Build the 2025 total from the 2024 amounts
A's decrease leaves of its 2024 amount, . B's increase makes of its 2024 amount, . Each new percent acts on the previous year's amount. Don't apply B's increase to , its 2023 amount. The 2025 total gives .
- Step 4
Read Process B's 2023 amount
Type the two equations in Desmos, one per line. Click their intersection, the point that satisfies both equations. Desmos shows . The second coordinate is , so the facility used megawatt-hours for Process B in 2023. Grid in 4000.