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Exponential Growth Modeling

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Exponential Growth Modelling

Graph showing exponential growth curve

📚 Part 1: Understanding Exponential Growth

1. The exponential growth formula is y = a × b^x. What does each variable represent?

a = _______________

b = _______________

x = _______________

y = _______________

2. Which of these situations shows exponential growth?

A car travelling at constant speed

Money earning compound interest

A phone plan with a fixed monthly fee

Bacteria doubling every hour

3. A population starts at 500 and doubles every 3 years. Complete the table:

Year 0: 500

Year 3: _______

Year 6: _______

Year 9: _______

4. In exponential growth, what is special about the ratio between consecutive values?

🧮 Part 2: Substitution and Calculation

5. A bank account starts with $2000 and grows by 5% each year. The formula is y = 2000 × 1.05^x.

Calculate the account balance after:

2 years: y = 2000 × 1.05^2 = $__________

5 years: y = 2000 × 1.05^5 = $__________

6. A town's population follows the formula P = 8000 × 1.03^t, where t is years since 2020.

What will the population be in 2025 (t = 5)?

7. In the formula y = 150 × 2.5^x, identify:

Initial value: __________

Growth factor: __________

Percentage increase per period: __________%

📈 Part 3: Real-World Modelling

8. A social media post gets shared exponentially. It starts with 10 shares and triples every day.

a) Write the exponential formula: y = __________

b) How many shares after 4 days? __________

9. Compare linear vs exponential growth. A savings account starts with $1000.

Linear: Adds $50 each month

Exponential: Grows by 4% each month

Which will have more money after 2 years? Explain your reasoning.

10. Extension Challenge: A phone's value depreciates by 20% each year. If it costs $800 new, write a formula for its value after t years. Is this exponential growth or decay?

Formula: V = __________

Type: __________

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