oliver.shannon49
oliver.shannon49 2d ago • 0 views

Real-world examples of exponential growth and decay in Pre-Calculus

Hey everyone! 👋 Ever wondered where you see exponential growth and decay in the real world when you're doing Pre-Calculus? It's more common than you think! Here's a quick study guide and quiz to help you nail it! 🧮
🧮 Mathematics

1 Answers

✅ Best Answer
User Avatar
susan_lynch Dec 27, 2025

📚 Quick Study Guide

  • 📈 Exponential Growth occurs when a quantity increases over time. The general formula is $y = a(1 + r)^t$, where:
    • $a$ = initial amount
    • $r$ = growth rate (as a decimal)
    • $t$ = time
  • 📉 Exponential Decay occurs when a quantity decreases over time. The general formula is $y = a(1 - r)^t$, where:
    • $a$ = initial amount
    • $r$ = decay rate (as a decimal)
    • $t$ = time
  • 🦠 Population growth is a common example of exponential growth.
  • ☢️ Radioactive decay is a common example of exponential decay. The half-life formula is $N(t) = N_0 e^{-kt}$, where:
    • $N(t)$ = amount remaining after time $t$
    • $N_0$ = initial amount
    • $k$ = decay constant
    • $t$ = time
  • 💰 Compound Interest follows an exponential growth pattern. $A = P(1 + \frac{r}{n})^{nt}$, where:
    • $A$ = the future value of the investment/loan, including interest
    • $P$ = the principal investment amount (the initial deposit or loan amount)
    • $r$ = the annual interest rate (as a decimal)
    • $n$ = the number of times that interest is compounded per year
    • $t$ = the number of years the money is invested or borrowed for

🧪 Practice Quiz

  1. What is the general formula for exponential growth?
    1. $y = a(1 - r)^t$
    2. $y = a(1 + r)^t$
    3. $y = a(r - 1)^t$
    4. $y = ar^t$
  2. A population of bacteria doubles every hour. If the initial population is 50, what is the population after 3 hours?
    1. 100
    2. 200
    3. 400
    4. 800
  3. A radioactive substance has a half-life of 10 years. If you start with 200 grams, how much will remain after 30 years?
    1. 100 grams
    2. 50 grams
    3. 25 grams
    4. 12.5 grams
  4. Which of the following is an example of exponential decay?
    1. Compound interest
    2. Population growth
    3. Radioactive decay
    4. Inflation
  5. If a car depreciates at a rate of 15% per year, how much will a $20,000 car be worth after 5 years?
    1. $6,800
    2. $8,874
    3. $10,000
    4. $12,000
  6. An investment of $5000 earns 8% interest compounded annually. What will be the value of the investment after 10 years?
    1. $10,000
    2. $10,794.62
    3. $10,874.44
    4. $11,000
  7. The half-life of a certain isotope is 5 hours. What percentage of the initial amount remains after 15 hours?
    1. 50%
    2. 25%
    3. 12.5%
    4. 6.25%
Click to see Answers
  1. B
  2. C
  3. C
  4. C
  5. B
  6. C
  7. C

Join the discussion

Please log in to post your answer.

Log In

Earn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀