📊 Part 1: Function Identification

1. Which function represents exponential growth?

f(x) = x² + 3x - 2

f(x) = 2ˣ

f(x) = -x² + 5

f(x) = 3x + 1

2. A quadratic function has the form:

f(x) = ax² + bx + c

f(x) = abˣ

f(x) = mx + b

f(x) = x³ + 2x

3. Check all characteristics that apply to exponential functions:

Has a constant rate of change

Grows by multiplication

Has a horizontal asymptote

Has a vertex

4. Which function grows faster for large values of x?

f(x) = x²

f(x) = 3ˣ

They grow at the same rate

It depends on the value of x

🔍 Part 2: Analysis and Applications

5. A ball is thrown upward. Its height h(t) = -16t² + 32t + 6, where t is time in seconds. What type of function is this and what does it represent?

6. A bacteria population doubles every hour. If you start with 50 bacteria, write the exponential function that models this situation after t hours.

P(t) = ________________

7. Compare the growth patterns: Fill in the tables below and describe the difference.

Quadratic: f(x) = x²

x = 1: f(1) = ____ x = 2: f(2) = ____ x = 3: f(3) = ____ x = 4: f(4) = ____

Exponential: g(x) = 2ˣ

x = 1: g(1) = ____ x = 2: g(2) = ____ x = 3: g(3) = ____ x = 4: g(4) = ____

8. Describe the key difference in how these functions grow:

🎯 Part 3: Real-World Connections

9. Match each scenario with the correct function type:

A. The area of a square with side length s

B. Money earning compound interest

C. The path of a basketball shot

D. Population growth of rabbits

1. Exponential

2. Quadratic

3. Exponential

4. Quadratic

10. A company's profit follows the function P(x) = -2x² + 16x - 10, where x is the number of items sold (in hundreds). At what production level is profit maximized?

11. Explain why exponential functions are often used to model population growth, while quadratic functions are used to model projectile motion:

Quadratic vs Exponential Functions

Quadratic vs Exponential Functions

📊 Part 1: Function Identification

🔍 Part 2: Analysis and Applications

🎯 Part 3: Real-World Connections

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