Sizu Riatto
Algebra · Chapter 19

Linear vs Exponential Growth

Adding the same amount each step makes a straight line; multiplying by the same percentage makes a curve that starts slow and then runs away.

Home › Calculators › Linear vs Exponential Growth

Opens on Chapter 19’s example: two offers on $200 a month: $50 more each month, or 5% more each month.

Enter your numbers, then press Work it out.

How it works

Adding a fixed amount gives start + increase × n after n steps: a straight line. Growing by a percentage multiplies by (1 + r) each step, so after n steps it’s start × (1 + r)ⁿ, a curve whose own steps keep getting bigger. The percentage starts behind but always catches up eventually. The doubling time is the first n where (1 + r)ⁿ reaches 2; the rule of 72 estimates it as 72 ÷ the percentage. Shrinking by a percentage halves in a fixed number of steps too.

From the book, Chapter 19. After 12 months offer A is $800 and offer B $359.17; after 36, $2,000 against $1,158.36. B overtakes at month 56 and doubles after 15 months (the rule of 72 says 14.4). $400 losing 15% a year is worth $208.80 after 4 years and $177.48 after 5. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.