Growth and decay: B(t) = B0 · q^t
Tell linear, quadratic and exponential tables apart, find a doubling time and a half-life with the logarithm, and see where an exponential model stops being realistic.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- France: grade 8
- Germany: grade 10
- Syria: grade 12
- Palestine: grade 11
- Ukraine: grade 11
Guide
Growth by p % per step multiplies by the growth factor q = 1 + p100; decay by p % has q = 1 − p100. After t steps the amount is B(t) = B0·qt.
A table is exponential when the ratio of neighbouring values is constant. If the differences are constant it is linear; if the second differences are constant it is quadratic.
To find a time, solve qx = b with the logarithm: x = lg b/lg q. Use the calculator and round at the end.
A model only describes reality for a limited time. Always ask whether the predicted values still make sense.