Modelling Growth & Decay with Recursion (Grade 12)
Free printable Grade 12 General Mathematics worksheet: modelling real growth and decay (savings, populations, depreciation, managed populations) with arithmetic, geometric and first-order linear recurrence relations (ACMGM070, ACMGM074, ACMGM077).
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Grade 12 · Math worksheet
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Date
Math
Growth & Decay: Modelling with Recursion
Set up a recurrence relation for each real situation and compute the requested term. Linear (equal step) situations use arithmetic sequences; constant-factor growth or decay uses geometric sequences; a survival-plus-restock situation uses a first-order linear recurrence.
- 1.A savings account starts with $200 and $15 is added every week. Model the balance with a recurrence relation and find the balance after 10 weeks.
- 2.A savings account starts with $110 and $40 is added every week. Model the balance with a recurrence relation and find the balance after 8 weeks.
- 3.A savings account starts with $360 and $17 is added every week. Model the balance with a recurrence relation and find the balance after 10 weeks.
- 4.A bacterial colony starts at 285 cells and multiplies by 3 every hour. Model it with a recurrence relation and find the population after 3 hours.
- 5.A bacterial colony starts at 215 cells and multiplies by 2 every hour. Model it with a recurrence relation and find the population after 4 hours.
- 6.A bacterial colony starts at 180 cells and multiplies by 2 every hour. Model it with a recurrence relation and find the population after 3 hours.
- 7.A car worth $29000 loses 10% of its value each year (so it keeps 90%). Model the value with a recurrence relation and find its value after 2 years. Round to the nearest cent.
- 8.A car worth $41000 loses 20% of its value each year (so it keeps 80%). Model the value with a recurrence relation and find its value after 2 years. Round to the nearest cent.
- 9.A car worth $45000 loses 10% of its value each year (so it keeps 90%). Model the value with a recurrence relation and find its value after 2 years. Round to the nearest cent.
- 10.A trout lake starts with 368 fish. Each year 80% survive and 123 new fish are added. Model this with a first-order linear recurrence and find the number of fish after 2 years. Round to the nearest whole fish.
- 11.A trout lake starts with 505 fish. Each year 80% survive and 79 new fish are added. Model this with a first-order linear recurrence and find the number of fish after 2 years. Round to the nearest whole fish.
- 12.A trout lake starts with 242 fish. Each year 90% survive and 70 new fish are added. Model this with a first-order linear recurrence and find the number of fish after 3 years. Round to the nearest whole fish.
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