When the rule says how fast something changes from how much there is, you don’t need to solve it: step it. New amount = old amount + rate × step. Smaller steps, better answers.
Opens on Chapter 24’s example: a bathtub filling at 3 gallons a minute and leaking 0.1 × its volume, in one-minute steps for 10 minutes.
Enter your numbers, then press Work it out.
How it works
Euler's method takes the rate at the start of each step and assumes it holds for the whole step: new = old + rate × step. Where the rate falls as the amount rises (a leak, drag), the steps run a little ahead of the truth; halve the step and the error roughly halves. The level stops changing where in equals out (A − By = 0, so y = A ÷ B): the steady state. Logistic growth is slow, then fast, then levels off at the cap, growing fastest at half the cap. Savings and loans step a month at a time, exactly as a bank does.
From the book, Chapter 24. One-minute steps put the tub at 19.54 gallons after 10 minutes; the exact answer is 18.96, and half- and tenth-minute steps give 19.25 and 19.02. With drag, the fall levels off at 160 ft/s (about 109 mph). Savings reach $2,453.51 in a year. The loan takes 33 months, the last payment $234.23. The app reaches half the town after about 19.6 days; the reservoir settles at 125. Every chapter and its calculator →
Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. Functions can be typed as 16t², 6 + 48t − 16t^2, 1000e^(0.05t) or √x; answers are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.
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