Real World: Exponential Growth & Decay

ACT Math · Axiom Academy

One relationship — — runs bacteria colonies, compound interest, and radioactive medicine. Put it in your hands. A lab culture starts at 500 bacteria and doubles every 20 minutes — the ACT loves this shape because the same formula prices a savings account and times a medical isotope. A colony that doubles every 20 minutes Drag the clock forward and watch the population compound — each 20-minute tick doesn't ADD bacteria, it MULTIPLIES the current count by 2. That's the difference between growth and exponential growth. How long until your money doubles? 1 , 000 sits in an account paying annual interest, compounded monthly: . Drag the target balance and watch the model solve for t by taking of both sides. A medical dose that halves every 8 days A hospital orders of iodine-131 (half-life 8 days) for a treatment scheduled in the future. Drag time forward and watch the same doubling model run backward — each half-life cuts the dose in half, not to zero. One shape, two directions: . Base b>1 compounds UP (bacteria, investments, viral spread); base 0<b<1 decays DOWN (radioactive isotopes, medication clearing your system, a car's resale value). When the ACT asks you to solve for time , take or of both sides — that's the one move that unlocks every version of this question.

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