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Grade 9 · Geometric growth

Pattern laboratory: Compare repeated growth factors

Pattern laboratory investigation: compare repeated growth factors. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Pattern laboratory: Compare repeated growth factors. Complete periods: 0. Multiplier per period: 1.05. Current amount: 7. Final amount: 8.509Repeated multiplication at whole periods02468080160xHorizontal: complete periods · Vertical: amount
Changes occur at discrete equally spaced periods with one fixed rate and no added deposits or withdrawals. Rates are between −40% and +40%, ensuring a positive multiplier. This is a mathematical model, not a financial return forecast.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Complete periods
0
Multiplier per period
1.05
Current amount
7
Final amount
8.509

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

Repeated percentage change multiplies the latest amount by a fixed factor each period. This differs from adding the same absolute amount repeatedly. A positive rate gives growth and a negative rate gives decay, while the original amount scales the entire sequence. This investigation begins with initial amount = 7; percent change per period = 5; complete periods = 4. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

Aₙ = A₀(1+r/100)ⁿ

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Represent the given quantities

    Convert the signed percentage into one positive multiplier per complete period.

  2. STEP 2

    Follow the changing model

    Playback adds whole periods; each new amount multiplies the preceding amount by the same factor.

  3. STEP 3

    Check and explain the relationship

    Compare the final amount with the initial value and with a simple-interest calculation, which follows a different rule.

Your turn to explain

Make a prediction. Test your reasoning.

Pattern laboratory: Start with 7 and apply 5% change for 4 complete periods. Find the final amount.

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

7(1+5/100)^4 ≈ 8.509. Each period uses the latest amount.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 9 · Algebra

Turn repeated percentage growth into a multiplier

Model a constant percentage increase applied to the current amount.