Understanding Exponential Growth and Decay Concepts
This worksheet guides you through the principles of exponential growth and decay, emphasizing formulas, applications, and critical analysis of real-world scenarios.
1. Which of the following is the base of the natural logarithm used in exponential growth and decay formulas? (1 choice)
2. Which of the following are components of the exponential growth formula N(t) = N_0 × e^{kt}? (multiple choice)
3. Explain in your own words what exponential decay means and provide a real-world example.
4. List the formulas for: Exponential Growth, Exponential Decay.
Exponential Growth
Exponential Decay
5. What does the growth rate constant (k) determine in an exponential growth scenario? (1 choice)
6. Which of the following scenarios can be modeled using exponential decay? (multiple choice)
7. Calculate the amount of a radioactive substance remaining after 10 years if its half-life is 5 years and the initial amount is 100 grams.
8. If a population of bacteria doubles every 3 hours, what is the doubling time in terms of the growth rate constant (k)? (1 choice)
9. Which factor is most critical in determining whether a process is modeled by exponential growth or decay? (1 choice)
10. Design a real-world scenario where exponential growth or decay could be applied. Describe the situation, identify the variables involved, and explain how you would model it mathematically.
11. Compare and contrast exponential growth and decay, highlighting their key differences and similarities.
12. What is the relationship between the doubling time and the growth rate constant in exponential growth? (1 choice)
13. Analyze the following scenarios and identify which involve exponential growth: (multiple choice)
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