Lesson Plan
Exponential Scavenger Hunt
Students will be able to apply their knowledge of exponential growth and decay to solve real-world problems through an interactive scavenger hunt.
Understanding exponential growth and decay is crucial for analyzing various real-world phenomena, from population changes and financial investments to radioactive decay. This lesson provides an engaging way to solidify these concepts.
Audience
12th Grade Students
Time
30 minutes
Approach
Students will work in teams to solve a series of 12 problems hidden around the classroom.
Materials
Whiteboard or projector, Exponential Scavenger Hunt Clues, and Exponential Scavenger Hunt Answer Key
Prep
Prepare Materials
15 minutes
- Review the Exponential Scavenger Hunt Clues and Exponential Scavenger Hunt Answer Key.
- Print and cut out the 12 scavenger hunt clue cards.
- Strategically hide the clue cards around the classroom. Each clue's answer should lead to the location of the next clue.
- Ensure the final clue leads back to a designated
Step 1
Introduction and Rules
5 minutes
Begin by welcoming students and introducing the day's activity: the Exponential Scavenger Hunt.
Teacher (Script): "Good morning, class! Today, we're going to embark on an exciting journey to explore exponential growth and decay through a scavenger hunt! Your mission, should you choose to accept it, is to work in teams to solve a series of problems hidden around the classroom. Each correct answer will lead you to your next clue."
Divide the class into small teams (2-3 students per team). Explain the rules clearly:
* Teams will start at a designated location to receive their first clue.
* They must solve the problem on the clue card.
* The answer to the problem will tell them where to find the next clue (e.g., "If your answer is 12.34, find the card hidden under something red").
* The goal is to complete all 12 clues and arrive at the finish point.
* Emphasize the importance of showing work and collaborating within their teams.
Briefly review key concepts of exponential growth ($A = P(1+r)^t$) and decay ($A = P(1-r)^t$) as needed, perhaps using the Exponential Scavenger Hunt Slide Deck.
Step 2
Scavenger Hunt Begins
20 minutes
Distribute the first clue to each team (or instruct them where to find it). Circulate among the teams, providing guidance and support as needed. Encourage students to discuss strategies and help each other. Remind them to show their work on separate paper.
Teacher (Script): "Remember, teamwork makes the dream work! Discuss the problems with your teammates, check your calculations, and think critically about where your answer might lead you."
Monitor time closely. Announce remaining time at intervals (e.g., "10 minutes left!", "5 minutes left!").
Step 3
Wrap-up and Discussion
5 minutes
Once all teams have completed the hunt or time is called, gather the class for a brief discussion.
Teacher (Script): "Fantastic effort, everyone! Let's debrief. What were some of the challenges you faced? Which problems were particularly tricky, and how did you overcome them?"
Review the answers using the Exponential Scavenger Hunt Answer Key, clarifying any misconceptions. Celebrate the teams that successfully completed the hunt or made significant progress.
use Lenny to create lessons.
No credit card needed
Slide Deck
Welcome to the Exponential Scavenger Hunt!
Are you ready for a challenge?
Today, we're putting your knowledge of exponential growth and decay to the test in an exciting scavenger hunt!
Work in teams, solve problems, and find your next clue!
Welcome students and introduce the concept of the scavenger hunt. Explain it's a fun way to apply their knowledge.
Quick Review: Exponential Growth
What is it? When a quantity increases by a fixed percentage over regular intervals.
Formula: A = P(1 + r)^t
- A = Final Amount
- P = Principal (Initial Amount)
- r = Rate of Growth (as a decimal)
- t = Time (number of periods)
Think: Where do we see this in the real world?
Briefly review the core concepts of exponential growth. Ask students for real-world examples.
Quick Review: Exponential Decay
What is it? When a quantity decreases by a fixed percentage over regular intervals.
Formula: A = P(1 - r)^t
- A = Final Amount
- P = Principal (Initial Amount)
- r = Rate of Decay (as a decimal)
- t = Time (number of periods)
Think: Where do we see this in the real world?
Briefly review the core concepts of exponential decay. Ask students for real-world examples.
How to Play: The Rules!
- Teams: You'll be divided into small teams.
- Start: Each team gets a first clue.
- Solve: Work together to solve the problem on the clue card.
- Find: The answer will tell you where to find the next clue.
- Repeat: Continue until you've solved all 12 clues!
- Show Your Work! Use separate paper to record your steps.
Good luck, mathematicians!
Explain the rules clearly. Emphasize teamwork and showing work.
Activity
Exponential Scavenger Hunt Clues
Instructions: Solve each problem. Your answer will tell you where to find the next clue!
Clue 1
A population of rabbits is growing exponentially. There are initially 50 rabbits, and the population increases by 15% each year. How many rabbits will there be after 3 years? (Round to the nearest whole rabbit).
If your answer is 76, find the next clue taped to the back of the classroom door.
Clue 2
A new car depreciates at a rate of 12% per year. If the car was bought for $30,000, what will its value be after 4 years? (Round to the nearest dollar).
If your answer is $17,991, find the next clue under the teacher's desk.
Clue 3
An investment of $2,500 earns 6% interest compounded annually. How much will the investment be worth after 5 years? (Round to the nearest cent).
If your answer is $3,345.56, find the next clue on the whiteboard, near the top right corner.
Clue 4
The half-life of a certain radioactive substance is 10 days. If you start with 100 grams, how much will be left after 30 days? (Round to two decimal places).
If your answer is 12.50 grams, find the next clue inside a textbook on the math shelf (specifically, the one with a blue cover).
Clue 5
A town's population is growing at a rate of 2.5% per year. If the current population is 15,000, what will the population be in 10 years? (Round to the nearest whole person).
If your answer is 19,201, find the next clue on the bottom of the trash can.
Clue 6
You buy a laptop for $1,200. It loses 20% of its value each year. What is its value after 2 years? (Round to the nearest dollar).
If your answer is $768, find the next clue stuck to the back of the student projector screen.
Clue 7
Bacteria in a petri dish double every hour. If you start with 50 bacteria, how many will there be after 6 hours?
If your answer is 3,200, find the next clue inside the clock on the wall.
Clue 8
A chemical decays at a rate of 5% per minute. If you begin with 200 mg, how much remains after 15 minutes? (Round to two decimal places).
If your answer is 92.66 mg, find the next clue on the window sill, behind the third plant from the left.
Clue 9
An antique vase appreciates in value by 3% each year. If it was purchased for $500, how much will it be worth in 7 years? (Round to the nearest cent).
If your answer is $614.94, find the next clue taped underneath a random student chair.
Clue 10
The atmospheric pressure decreases by 4% for every 1000 feet increase in altitude. If the pressure at sea level is 1013 millibars, what is the pressure at 5000 feet? (Use t = 5 for 5000 feet, round to two decimal places).
If your answer is 826.00 millibars, find the next clue inside the marker tray of the whiteboard.
Clue 11
If you invest $10,000 at an annual interest rate of 8% compounded quarterly, how much money will you have after 2 years? (Hint: $n=4$, round to two decimal places).
If your answer is $11,716.59, find the next clue on the back of the fire extinguisher.
Clue 12
A certain type of mold grows by 25% per day. If you start with 10 square centimeters of mold, how many square centimeters will there be after 5 days? (Round to two decimal places).
If your answer is 30.52 square centimeters, congratulations! You have completed the hunt! Return to your teacher for further instructions.
Answer Key
Exponential Scavenger Hunt Answer Key
Here are the solutions and steps for each clue in the scavenger hunt.
Clue 1: Rabbit Population Growth
Problem: A population of rabbits is growing exponentially. There are initially 50 rabbits, and the population increases by 15% each year. How many rabbits will there be after 3 years? (Round to the nearest whole rabbit).
Formula: $A = P(1+r)^t$
- P = 50
- r = 0.15
- t = 3
Calculation:
$A = 50(1 + 0.15)^3$
$A = 50(1.15)^3$
$A = 50(1.520875)$
$A = 76.04375$
Answer: Approximately 76 rabbits. (Leads to: back of the classroom door)
Clue 2: Car Depreciation
Problem: A new car depreciates at a rate of 12% per year. If the car was bought for $30,000, what will its value be after 4 years? (Round to the nearest dollar).
Formula: $A = P(1-r)^t$
- P = $30,000
- r = 0.12
- t = 4
Calculation:
$A = 30000(1 - 0.12)^4$
$A = 30000(0.88)^4$
$A = 30000(0.59969536)$
$A = 17990.8608$
Answer: $17,991. (Leads to: under the teacher's desk)
Clue 3: Investment Growth
Problem: An investment of $2,500 earns 6% interest compounded annually. How much will the investment be worth after 5 years? (Round to the nearest cent).
Formula: $A = P(1+r)^t$
- P = $2,500
- r = 0.06
- t = 5
Calculation:
$A = 2500(1 + 0.06)^5$
$A = 2500(1.06)^5$
$A = 2500(1.3382255776)$
$A = 3345.563944$
Answer: $3,345.56. (Leads to: on the whiteboard, near the top right corner)
Clue 4: Radioactive Decay (Half-Life)
Problem: The half-life of a certain radioactive substance is 10 days. If you start with 100 grams, how much will be left after 30 days? (Round to two decimal places).
Formula: $A = P(1/2)^{(t/h)}$, where h is the half-life.
- P = 100
- t = 30
- h = 10
Calculation:
$A = 100(1/2)^{(30/10)}$
$A = 100(0.5)^3$
$A = 100(0.125)$
$A = 12.50$
Answer: 12.50 grams. (Leads to: inside a textbook on the math shelf (specifically, the one with a blue cover))
Clue 5: Town Population Growth
Problem: A town's population is growing at a rate of 2.5% per year. If the current population is 15,000, what will the population be in 10 years? (Round to the nearest whole person).
Formula: $A = P(1+r)^t$
- P = 15,000
- r = 0.025
- t = 10
Calculation:
$A = 15000(1 + 0.025)^{10}$
$A = 15000(1.025)^{10}$
$A = 15000(1.2800845447)$
$A = 19201.2681705$
Answer: Approximately 19,201 people. (Leads to: on the bottom of the trash can)
Clue 6: Laptop Depreciation
Problem: You buy a laptop for $1,200. It loses 20% of its value each year. What is its value after 2 years? (Round to the nearest dollar).
Formula: $A = P(1-r)^t$
- P = $1,200
- r = 0.20
- t = 2
Calculation:
$A = 1200(1 - 0.20)^2$
$A = 1200(0.80)^2$
$A = 1200(0.64)$
$A = 768$
Answer: $768. (Leads to: stuck to the back of the student projector screen)
Clue 7: Bacteria Growth
Problem: Bacteria in a petri dish double every hour. If you start with 50 bacteria, how many will there be after 6 hours?
Formula: $A = P(2)^{t/k}$, where k is the doubling time (1 hour in this case).
- P = 50
- t = 6
- k = 1
Calculation:
$A = 50(2)^{(6/1)}$
$A = 50(2)^6$
$A = 50(64)$
$A = 3200$
Answer: 3,200 bacteria. (Leads to: inside the clock on the wall)
Clue 8: Chemical Decay
Problem: A chemical decays at a rate of 5% per minute. If you begin with 200 mg, how much remains after 15 minutes? (Round to two decimal places).
Formula: $A = P(1-r)^t$
- P = 200
- r = 0.05
- t = 15
Calculation:
$A = 200(1 - 0.05)^{15}$
$A = 200(0.95)^{15}$
$A = 200(0.46329124)$
$A = 92.658248$
Answer: 92.66 mg. (My apologies, another slight discrepancy. The clue states 93.30 mg. I will adjust the clue to 92.66 mg for consistency.) (Leads to: on the window sill, behind the third plant from the left)
Clue 9: Antique Vase Appreciation
Problem: An antique vase appreciates in value by 3% each year. If it was purchased for $500, how much will it be worth in 7 years? (Round to the nearest cent).
Formula: $A = P(1+r)^t$
- P = $500
- r = 0.03
- t = 7
Calculation:
$A = 500(1 + 0.03)^7$
$A = 500(1.03)^7$
$A = 500(1.229873867)$
$A = 614.9369335$
Answer: $614.94. (Leads to: taped underneath a random student chair)
Clue 10: Atmospheric Pressure Decay
Problem: The atmospheric pressure decreases by 4% for every 1000 feet increase in altitude. If the pressure at sea level is 1013 millibars, what is the pressure at 5000 feet? (Use t = 5 for 5000 feet, round to two decimal places).
Formula: $A = P(1-r)^t$
- P = 1013
- r = 0.04
- t = 5 (since 5000 feet is 5 * 1000 feet increments)
Calculation:
$A = 1013(1 - 0.04)^5$
$A = 1013(0.96)^5$
$A = 1013(0.8153726976)$
$A = 825.996167$
Answer: 826.00 millibars. (Another discrepancy! The clue states 823.10 millibars. I will adjust the clue to 826.00 millibars for consistency.) (Leads to: inside the marker tray of the whiteboard)
Clue 11: Compounded Quarterly Investment
Problem: If you invest $10,000 at an annual interest rate of 8% compounded quarterly, how much money will you have after 2 years? (Hint: $n=4$, round to two decimal places).
Formula: $A = P(1 + r/n)^{nt}$
- P = $10,000
- r = 0.08
- n = 4
- t = 2
Calculation:
$A = 10000(1 + 0.08/4)^{(4*2)}$
$A = 10000(1 + 0.02)^8$
$A = 10000(1.02)^8$
$A = 10000(1.171659381)$
$A = 11716.59381$
Answer: $11,716.59. (Leads to: on the back of the fire extinguisher)
Clue 12: Mold Growth
Problem: A certain type of mold grows by 25% per day. If you start with 10 square centimeters of mold, how many square centimeters will there be after 5 days? (Round to two decimal places).
Formula: $A = P(1+r)^t$
- P = 10
- r = 0.25
- t = 5
Calculation:
$A = 10(1 + 0.25)^5$
$A = 10(1.25)^5$
$A = 10(3.0517578125)$
$A = 30.517578125$
Answer: 30.52 square centimeters. (Leads to: completion of the hunt, return to teacher)