← Day 18
UNIT 6 / 8 · LESSON 3 / 4 · 26 MINUTES

Recognize multiplicative change

Linear change adds a fixed amount. Exponential change multiplies by a fixed factor over equal intervals.

01 / THE METHOD

Make it repeatable

  1. Check equal intervals for common differences or common ratios.
  2. Translate a percent increase into a factor above 1 and a decrease into a factor below 1.
  3. Keep the time unit in the exponent.
  4. Evaluate a contextual result and check whether a linear model could fit.
02 / WORKED EXAMPLE

Watch the method in action

A quantity starts at 200 and grows by 10% each year. Find the value after two years.
  1. The yearly factor is 1.10.
  2. Write 200(1.10)^2.
  3. Evaluate: 242.

The second increase acts on 220, so the result is 242 rather than 240.

03 / QUICK CHECK

Try it yourself

Which model represents the quantity after t years?

04 / PRACTISE AND CHECK

Apply the method to real questions

Start with guided questions and feedback. Then take a fresh independent set without hints. Reach at least 80% on that set to record this lesson.

Pass the quick check above to unlock practice.