Grade 9 · Compare repeated growth factors · 67 of 750
Compare repeated growth factors · practice 7
Start at 8 and apply a -35% change during each of 7 complete periods. Find the final amount. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Start at 8 and apply a -35% change during each of 7 complete periods. Find the final amount.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Apply the same multiplier to the latest amount each period.
Work through the reasoning
Step 1
Translate the givens
The multiplier per period is 1 + -35/100 = 0.65.
Step 2
Calculate with the model
After one period the amount is 8 × 0.65 = 5.2; after 7 periods it is 8 × (0.65)^7.
Step 3
Check and interpret
Evaluate the product to get approximately 0.39218. Dividing by the positive multiplier 7 times returns 8; adding the same original percentage amount repeatedly would be a different model.
The answer
8(1 + -35/100)^7 ≈ 0.39218.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
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. Starting quantities: Initial amount = 8; Percent change per period = -35; Complete periods = 7.
Aₙ = A₀(1+r/100)ⁿ
03 · Reflect and transfer
Explain what changes and why.
Why is repeated percent change multiplicative rather than repeated addition of the first change?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.