exponential function word problems worksheet

Lemon

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03-02-2025

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This worksheet provides a range of word problems involving exponential functions, designed to challenge and enhance your understanding. Remember to identify the initial value, growth/decay factor, and time variable to successfully solve these problems. We'll cover various applications, from population growth to compound interest.

Section 1: Population Growth and Decay

Problem 1: A bacterial colony starts with 100 bacteria and doubles in size every hour. How many bacteria will there be after 5 hours? After 10 hours? Write an equation representing the bacterial population (P) as a function of time (t) in hours.

Problem 2: The population of a town is decreasing at a rate of 5% per year. If the current population is 10,000, what will the population be in 3 years? In 10 years? What equation models this population decline?

Problem 3: A radioactive substance decays at a rate proportional to the amount present. If the initial amount is 100 grams and it decays to 50 grams in 2 years, what is the half-life of the substance (the time it takes for half the substance to decay)? What will be the amount remaining after 5 years?

Section 2: Compound Interest

Problem 4: You invest $1,000 in a savings account that pays 4% annual interest, compounded annually. How much money will you have in the account after 5 years? After 10 years? What equation describes your account balance (A) after t years?

Problem 5: Suppose the interest in Problem 4 is compounded quarterly (four times per year). How does this change the calculation, and what will be the balance after 5 years and 10 years?

Problem 6: You want to have $5,000 in your savings account in 3 years. If the account pays 6% annual interest compounded monthly, how much money should you deposit today?

Section 3: Other Applications

Problem 7: The value of a car depreciates at a rate of 15% per year. If the car was initially purchased for $25,000, what will its value be after 4 years?

Problem 8: The intensity of light decreases exponentially as it passes through water. If the intensity is reduced to 25% of its initial value after passing through 1 meter of water, what percentage of the initial intensity remains after passing through 3 meters of water?

Solutions (For Instructor Use)

This section will contain the detailed solutions to each problem. These solutions should include step-by-step calculations and explanations, reinforcing the concepts covered in each problem. (Solutions would be added here in a real worksheet.)

Further Exploration

Consider researching the following topics to deepen your understanding of exponential functions and their applications:

• Logistic Growth: Models situations where growth is initially exponential but levels off due to limiting factors.
• Differential Equations: Equations that describe the rate of change of a quantity, often used to model exponential growth and decay.
• Real-World Applications: Explore exponential functions in various fields like medicine, finance, and environmental science.

This worksheet aims to provide a solid foundation in solving exponential function word problems. By working through these examples and understanding the underlying principles, you'll gain valuable problem-solving skills applicable to various real-world scenarios. Remember to practice regularly to solidify your understanding.