Exponential Growth and Decay Explained Simply

Exponential Growth and Decay Explained Simply

Grade 7 Mathematics Understanding patterns that grow and shrink rapidly

What is Exponential Growth?

When something grows by the same percentage each time period The growth rate stays constant, but the actual amount grows faster and faster Like a snowball rolling downhill - it gets bigger and bigger more quickly

Paper Folding Challenge

Fold a piece of paper in half Count the layers: 1 fold = 2 layers Fold again: 2 folds = 4 layers Continue folding and counting layers What pattern do you notice?

Real-World Examples of Exponential Growth

Population of bacteria doubling every hour Money growing with compound interest Viral videos spreading on social media Chain letters or pyramid schemes

Exponential Growth Graph

What is Exponential Decay?

When something decreases by the same percentage each time period The decay rate stays constant, but it shrinks faster at first Like a hot cup of coffee cooling down - loses heat quickly at first, then more slowly

Growth vs. Decay Comparison

{"left":"Exponential Growth\nStarts slow, speeds up\nGoes up and up\nJ-shaped curve","right":"Exponential Decay\nStarts fast, slows down\nGoes down toward zero\nBackwards J-shaped curve"}

Real-World Examples of Exponential Decay

Car value decreasing over time Medicine leaving your body Radioactive materials breaking down Phone battery losing charge

Think and Discuss

A rumor spreads through your school On day 1: 2 people know On day 2: 4 people know On day 3: 8 people know Is this exponential growth or decay? How many people will know on day 5?

Key Takeaways

Exponential patterns involve constant percentage changes Growth: starts slow, then accelerates rapidly Decay: starts fast, then slows down toward zero These patterns appear everywhere in real life Understanding them helps us make better predictions