Year 10 Maths • AC9M10A04 • Authored homework
Applied growth and decay modelling
Use mathematical modelling to solve applied growth and decay problems, including repeated percentage change, compound interest, depreciation and checking the reasonableness of predictions. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Write the multiplier for a 7% increase.
Write the multiplier for a 15% decrease.
Increase $400 by 8%.
Decrease $1200 by 10%.
What does the base in A = P(1 + r)^n represent?
What does n represent in a compound growth model?
State whether multiplying by 0.92 represents growth or decay.
Why is repeated 10% increase not the same as adding 10 percentage points each year?
Correct this error: “A 20% decrease then a 20% increase returns to the original value.”
Give one situation where a decay model may be useful.
Part B
Long-answer questions
A bank account has $1500 earning 4% compound interest per year. Find the balance after 5 years.
A laptop costs $1800 and depreciates by 18% per year. Estimate its value after 3 years.
A population of 12 000 grows by 2.5% each year. Write a model and predict the population after 6 years.
Compare simple interest and compound interest for $2000 at 5% over 4 years.
A medicine level in the body decreases by 30% each hour. Model the amount remaining from an initial 200 mg after 5 hours.
A city’s waste output decreases by 6% each year after a recycling program. Estimate the percentage remaining after 4 years.
Explain the assumptions and limitations in a repeated percentage growth model.
A student uses 1.12 as the multiplier for a 12% decrease. Explain and correct the mistake.
Create a finance or science modelling problem involving repeated percentage change and solve it fully.
Write a full modelling response with variables, equation, substitution, answer, interpretation and limitation.
Part C
Research and understanding task
Choose a real repeated percentage context, such as savings, depreciation, population, medicine, inflation or energy use. Build a model, calculate at least three time points, and discuss whether the model is realistic.