Piggies and Pools

Learning Focus

Represent situations with different types of growth and compare models over time.

Big idea

• Arithmetic / linear: add a constant (pennies each day, gallons per minute)
• Geometric / exponential: multiply by a constant factor (interest, percent drain)
• Some contexts are discrete (whole days); others are continuous (time in minutes)

Worked example

Piggy bank: start $5$ pennies, add $3$ each day $\Rightarrow f(n)=5+3n$.

Bank account: start \50$, grow by$3%$each month$\Rightarrow A(m)=50(1.03)^m$.

Takeaways

• Domain matters: counting days vs measuring continuous time.
• Same “story family” can look linear or exponential depending on add vs multiply.