Exponential Scavenger Hunt Lesson Plan Mission Briefing
Exponential Scavenger Hunt
Status: Active
Duration: 30 Min
Objective
Students will apply knowledge of exponential growth and decay to solve real-world problems through an interactive scavenger hunt, reinforcing their ability to model data and predict future outcomes.
Audience
12th Grade Students
Why This Matters
Understanding exponential growth and decay is crucial for analyzing various real-world phenomena, from population changes and financial investments to radioactive decay and medical dosages. This lesson moves beyond textbook problems into a dynamic, movement-based application.
Pre-Mission Prep
Review: Go over the Scavenger Hunt Clues and Answer Key to familiarize yourself with the path.
Print: Print and cut out the 12 clue cards. Using cardstock is recommended for durability.
Setup: Hide clues according to the locations specified in the clues. Each answer leads to the *next* location.
Check: Ensure the final clue (Clue 12) points students back to you or a "Mission Complete" zone.
Mission Timeline
5m
Introduction & Rules
Welcome agents and brief them on the objectives.
Divide the class into teams of 2-3. Explain that correct answers reveal the location of the next clue. Review the primary formulas:
Growth: \(A = P(1+r)^t\)
Decay: \(A = P(1-r)^t\)
Teacher Script: "Today, we're embarking on a journey! Your mission is to work in teams to solve 12 hidden problems. Each answer is a key that unlocks your next destination."
20m
The Hunt is On
Monitor progress and provide tactical support.
Distribute the first clue to each team. Circulate to provide guidance. Ensure students are recording their work on separate paper for verification.
Teacher Script: "Remember, teamwork makes the dream work! Check your calculations carefully—one wrong turn could lead you to a dead end!"
5m
Mission Debrief
Review solutions and key learnings.
Gather the class. Discuss challenges and tricky problems. Use the Answer Key to clarify misconceptions.
Teacher Script: "Fantastic effort! What was the hardest variable to identify? Which scenarios surprised you?"
Required Equipment
Clue Card Set (12 cards)
Answer Key
Student Scratch Paper
Projector / Slide Deck
Exponential Hunt Slides Exponential
Scavenger Hunt
Your mission: Solve 12 mathematical mysteries to navigate the classroom and complete the objective.
Status: Ready
Target: 12th Grade
Briefing: Exponential Growth
Growth occurs when a quantity increases by a fixed percentage over regular intervals.
\[A = P(1 + r)^t\]
Legend
A Final Amount
P Initial (Principal)
r Rate (as decimal)
t Time Periods
Briefing: Exponential Decay
Decay occurs when a quantity decreases by a fixed percentage over regular intervals.
\[A = P(1 - r)^t\]
Legend
A Final Amount
P Initial (Principal)
r Rate (as decimal)
t Time Periods
Protocol & Rules
01
TEAMS: Move in squads of 2-3 agents.
02
SOLVE: Compute the answer precisely. Use scratch paper.
03
LOCATE: Your answer reveals the next clue's position.
Critical Requirement
You must show all work to receive credit for the mission.
GO! GO! GO!
Exponential Hunt Clue Cards Clue 01
Subject: Rabbit Population
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 02
Subject: Vehicle Assets
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 03
Subject: Capital Investment
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 04
Subject: Isotope Decay
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 blue math textbook on the shelf.
Clue 05
Subject: Urban Expansion
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 06
Subject: Tech Obsolescence
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 projector screen.
Clue 07
Subject: Biological Doubling
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 08
Subject: Compound Dilution
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 09
Subject: Artifact Value
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).
Exponential Hunt Answer Key Mission Clearance
Official Answer Key: Exponential Scavenger Hunt
Confidential
Teacher Resource
Clue 1: Rabbit Population
Formula: \(A = P(1+r)^t\)
\(A = 50(1.15)^3 \approx 76.04\)
Answer: 76
Location: Back of classroom door
Clue 2: Car Depreciation
Formula: \(A = P(1-r)^t\)
\(A = 30000(0.88)^4 \approx 17990.86\)
Answer: $17,991
Location: Under teacher's desk
Clue 3: Investment
Formula: \(A = P(1+r)^t\)
\(A = 2500(1.06)^5 \approx 3345.56\)
Answer: $3,345.56
Location: Top right of whiteboard
Clue 4: Half-Life
Formula: \(A = P(0.5)^{t/h}\)
\(A = 100(0.5)^{30/10} = 12.5\)
Answer: 12.50 g
Location: Inside blue math textbook
Clue 5: Town Population
Formula: \(A = P(1+r)^t\)
\(A = 15000(1.025)^{10} \approx 19201.27\)
Answer: 19,201
Location: Bottom of trash can
Clue 6: Laptop Depreciation
Formula: \(A = P(1-r)^t\)
\(A = 1200(0.80)^2 = 768\)
Answer: $768
Location: Back of projector screen
Clue 7: Bacteria Growth
Formula: \(A = P(2)^t\)
\(A = 50(2)^6 = 3200\)
Answer: 3,200
Location: Inside clock on the wall
Clue 8: Chemical Decay
Formula: \(A = P(1-r)^t\)
\(A = 200(0.95)^{15} \approx 92.66\)
Answer: 92.66 mg
Location: Window sill, behind 3rd plant
Clue 9: Antique Vase
Formula: \(A = P(1+r)^t\)
\(A = 500(1.03)^7 \approx 614.94\)
Answer: $614.94
Location: Taped under random chair
Clue 10: Pressure Decay
Formula: \(A = P(1-r)^t\)
\(A = 1013(0.96)^5 \approx 826.00\)
Answer: 826.00 mb
Location: Whiteboard marker tray
Clue 11: Quarterly Compound
Formula: \(A = P(1+r/n)^{nt}\)
\(A = 10000(1.02)^8 \approx 11716.59\)
Answer: $11,716.59
Location: Back of fire extinguisher
Clue 12: Mold Growth
Formula: \(A = P(1+r)^t\)
\(A = 10(1.25)^5 \approx 30.52\)
Answer: 30.52 cm²
Location: Mission Completion
