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Exponential Growth Modeling
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Exponential Growth Modeling
Show your working for calculations. Round money to the nearest cent and people or shares to the nearest whole number.
Understanding Exponential Growth
1.For the model y = a × bˣ, state what a, b, x and y represent.
2.Which two situations are examples of exponential growth? Select both.
- A cyclist travels 12 km every hour.
- A savings balance earns compound interest at a fixed percentage.
- A shop charges a fixed $8 delivery fee on every order.
- A yeast culture increases by a fixed percentage each hour.
3.A wildlife reserve begins with 240 wallabies. The population doubles every four years. Find the population at year 4, year 8 and year 12.
4.For an exponential growth model, what stays constant when you divide each value by the previous value, assuming equal time steps?
Substitution and Calculation
5.An investment of $1,600 grows by 6% each year, so its value after x years is A = 1600 × 1.06ˣ. Calculate its value after 3 years and after 6 years.
6.A regional town's population is modelled by P = 12,500 × 1.025ᵗ, where t is the number of years after 2022. Estimate the population in 2027, rounding to the nearest person.
7.For the model N = 90 × 1.4ˣ, identify the initial value, growth factor and percentage increase per time period.
Real-World Exponential Models
8.A video has 18 views at the start of a sharing campaign. The number of views doubles each day. Write a formula for the views after d days, then calculate the number after 5 days.
9.Oliver compares two ways to grow $1,200 over 18 months. Option A adds $35 each month. Option B grows by 3% each month. Which option gives the greater balance after 18 months? Show or describe how you decided.
10.A laptop costs $1,250 when new and loses 15% of its value each year. Write a model for its value after t years and state whether this is growth or decay.
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