Purpose: Verify Chapter 3 mastery (exponent laws, exponential graphs) before tackling exponential equations and modelling.
Prerequisite Skills
Question 1 [3 marks]
Express each as a power of 2: \( 16, 64, 1, \tfrac{1}{8} \).
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Question 2 [3 marks]
Solve the linear equation \( 3x + 5 = 2x - 7 \).
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Question 3 [3 marks]
If \( y = 2 \cdot 3^x \), find \( y \) when \( x = 0, 1, 2, 3 \). Identify the common ratio.
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Question 4 [3 marks]
Convert these percent rates to decimals and 1+r form: 8%, 0.5%, 12.5%.
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Question 5 [2 marks]
Evaluate \( 4 \cdot 3^2 \) and \( (4 \cdot 3)^2 \). Are they equal? Explain.
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Question 6 [3 marks]
A pizza loses heat: at 0 min it is 80°C, at 5 min it is 60°C. Estimate (with a calculator) what kind of decay model fits and what the temperature is at 10 min if decay is exponential with the same ratio.
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Reflection
Question 7 [Reflection]
When you see a real-world problem like "doubles every 4 hours" or "decays at 5% per year", what is the first thing you write down? Reflect on your typical approach.
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