Story Problem

Behi Rabbani, MD

True stories that make math and science clear. Story Problem is for curious adults, parents helping with schoolwork, and anyone ready to understand the subjects they may have missed the first time around. No notes. No prerequisites. Just listen.

  1. 3d ago

    Exponential Growth — Look for the Operation, Not the Answer | Office Hours 9

    Send us Fan Mail The chain reaction that ran under a Chicago squash court hides one of the most useful ideas in math: repeated multiplication. In this Office Hours companion to Episode 9, we take that idea out of the reactor and make it something you can use on a savings account, a population, or any number that grows by the same percentage each step. You won't need to memorize a formula. Instead we build four moves you can run on any growth problem: identify the step, find the multiplier and compare it with one, run the pattern forward, and work backward to find how many steps it takes. Along the way we use the Rule of 70 to estimate doubling time in your head, and a logarithm to pin down an exact answer — the same move from our carbon-clock episode. The one question to carry with you: what happens from one step to the next — are we adding the same amount, or multiplying by the same factor? Answer that first, and the rest follows. Practice the ten Study Hall problems for this episode at storyproblem.org. Chapters (0:00) The Question Before the Calculation (1:14) Identify the Step (3:37) Find the Multiplier and Compare It With One (6:05) Run It Forward Without Losing the Meaning (8:45) Work Backward and Check the Scale (11:14) Take the Habit With You

  2. 6d ago

    The Nuclear Reaction — When the Curve Turns Up

    Send us Fan Mail On December 2, 1942, a small group of scientists gathered beneath the stands of an abandoned football stadium in Chicago. Nearby stood a man with an axe. His job was simple: if something went wrong, cut the rope. What they were watching was the world's first controlled nuclear chain reaction. But underneath the physics was a remarkably simple mathematical idea: what happens when one event creates more than one new event? In this episode of Story Problem, we follow the numbers behind a chain reaction—from a single neutron to a curve that suddenly begins to climb. We look at the one number that determines whether a reaction dies out, stays steady, or grows, and why the same basic mathematics appears far beyond nuclear physics. This is a story about multiplication, exponential growth, and the moment when a small change in a number can completely change what happens next. Chapters 00:00 — The Man With the Axe 02:10 — What Is a Chain Reaction? 03:49 — The Number That Matters 06:08 — December 2, 1942 07:40 — The Curve Turns Up 10:04 — Why This Is a Math Story

  3. Sep 11

    Reading the Carbon Clock — Three Moves for Exponential Decay | Office Hours 8

    Send us Fan Mail How do you solve a carbon-14 problem without getting lost in the formula? In this Office Hours episode, we build a compact toolkit for exponential-decay problems: Count. Locate. Reverse. First, count the halvings when the fraction remaining is familiar. Next, locate an unfamiliar percentage between known half-life landmarks. Finally, run the clock backward with a logarithm to find the age of a sample. Using examples involving ancient bones, Ötzi the Iceman, and the Dead Sea Scrolls, we learn how to estimate before calculating, recognize unreasonable answers, and decide whether carbon-14 is the right clock for the timescale. The goal is not to memorize a separate formula for every problem. It is to recognize which move the problem is asking for. Try the ten accompanying Study Hall problems at storyproblem.org. Chapters 00:00 — Reading the Carbon Clock 00:56 — The Carbon-14 Toolkit 01:44 — Start With One Problem 03:56 — Move 1: Count the Halvings 06:01 — Move 2: Locate Between the Landmarks 08:21 — Move 3: Run the Clock Backward 12:13 — Match the Clock to the Timescale 13:28 — Count. Locate. Reverse.

  4. Sep 6

    The Carbon Clock: Exponential Decay and Radiocarbon Dating

    Send us Fan Mail How can a small piece of bone reveal when an organism lived thousands of years ago? In this episode of Story Problem, we explore how chemist Willard Libby developed radiocarbon dating and how carbon-14 acts like a clock inside material that was once alive. We begin with half-life and exponential decay: why carbon-14 decreases by half every 5,730 years and how that repeated halving produces an exponential equation. Then we work backward. When a sample does not contain a simple fraction such as one-half or one-quarter, a logarithm allows us to calculate how many half-lives have passed—and estimate the sample’s age. We also examine how scientists tested and calibrated radiocarbon dating, what the method made possible in archaeology, and why every radioactive dating method has a limited range. No advanced math background is required. We build the equation one part at a time and explain what each number means. Study Hall problems and the answer key are available at storyproblem.org. CHAPTERS 00:00 Introduction 01:00 The Two Tools You Already Have 01:50 Why the Question Was So Hard 02:53 Libby’s Insight 04:30 Half-Life and Exponential Decay 06:03 Working Backward with a Logarithm 13:34 Testing and Calibrating the Clock 15:52 What Radiocarbon Dating Made Possible 17:44 Every Dating Method Has a Range 19:11 Reading the Age From What Remains

  5. Sep 4

    Logarithms: Ask the Exponent | Office Hours 7

    Send us Fan Mail Logarithms become much easier when you understand the question they are asking: What exponent produced this number? In this Office Hours episode, Behi explains logarithms in plain language and shows how they are connected to exponents. You’ll learn how to move between exponential and logarithmic form, understand negative logarithms, compare measurements on logarithmic scales, and make sense of the product and quotient rules. Then we work through the two challenge problems from Episode 7’s Study Hall in depth. In Problem 9, we use logarithms to find the time hidden inside an exponential-growth model. In Problem 10, we combine two logarithms, solve the resulting quadratic equation, and check why one of the possible answers is not allowed. The guiding method throughout the episode is simple: Ask what the problem wants. Translate the expression. Compare the values. Solve—and check the answer. Find the complete Study Hall problems at storyproblem.org.

  6. Sep 1

    The Earthquake that Needed a Number

    Send us Fan Mail On March 10, 1933, a powerful earthquake struck Long Beach, California. Buildings cracked, schools were badly damaged, and descriptions of the destruction poured in. But those descriptions raised a difficult question: how could scientists compare one earthquake with another using something more consistent than reports of damage? At Caltech, Charles Richter and his colleagues were already working through rooms full of paper seismograms, looking for a reliable way to compare earthquakes. Their solution depended on logarithms. In this episode of Story Problem, we follow the development of earthquake magnitude and use it to understand what a logarithm actually tells us. Exponents build numbers through repeated multiplication. Logarithms reverse the question: they tell us which exponent produced the number. Along the way, we see why logarithmic scales are useful when measurements span an enormous range—and why a magnitude number only matters when we understand what it represents. Chapters: 00:00 Long Beach, March 10, 1933 01:57 Part 1: The Problem with Describing Damage 03:14 Part 2: A Room Full of Paper Records 06:28 Part 3: What a Logarithm Actually Says 10:41 Part 4: Building the Number 13:17 Part 5: Back to Long Beach 16:09 Give the Number Its Meaning

  7. Aug 27

    Scientific Notation and Exponents | Office Hours 6

    Send us Fan Mail Scientific notation is more than a shorter way to write very large and very small numbers. It helps you recognize the scale of a problem, organize the calculation, and check whether your answer makes sense. In this Office Hours episode, we work through positive and negative exponents, multiplication and division in scientific notation, and a practical method for setting up problems before doing the arithmetic. We also solve two problems from the Episode 6 Story Sheet—including estimating how many molecules were in Benjamin Franklin’s teaspoon of oil. The method to remember is simple: figure out the scale, move the numbers, and check the exponent. Download the Story Sheet and follow along at storyproblem.org. CHAPTERS 02:01 — Why Scientific Notation Is Useful 03:08 — Positive and Negative Exponents 04:18 — Using Exponents to Check Scale 05:10 — Multiplying and Dividing in Scientific Notation 06:32 — Set Up the Problem Before Doing the Arithmetic 07:27 — Problem 9: How Many Molecules Were in the Teaspoon? 08:48 — Problem 10: Solve for the Exponent 13:50 — The Method to Remember

  8. Aug 24

    The Teaspoon That Almost Measured a Molecule

    Send us Fan Mail In 1773, Benjamin Franklin poured a teaspoon of oil onto a pond at Clapham Common and watched it spread across the water, leaving an unexpectedly large area smooth behind it. Franklin recorded what he saw—but stopped just short of the calculation that could have taken him into the invisible world. In this episode, we finish that calculation. Using scientific notation, powers of ten, and order-of-magnitude thinking, we estimate the thickness of Franklin’s oil film and discover that an ordinary teaspoon can bring us remarkably close to the scale of a molecule. Along the way, we learn three practical moves: figure out the scale first, work the exponents, and compare the answer with something known. Then we travel from one tiny molecule to an entire mole—crossing thirty-two powers of ten without ever needing to write out all the zeros. CHAPTERS 00:14 A Teaspoon and Something Invisible 02:07 The Smooth Wake 04:18 The Pond at Clapham Common 06:04 The Measurement Franklin Didn’t Make 07:59 The Long Decimal 09:25 Figure Out the Scale First 10:38 Work the Exponents 11:47 Compare It 13:08 A Kitchen, a Tin Trough, and a New Science 15:38 From One Molecule to a Mole 17:17 Why the Scale Matters 18:23 The Number Derived from the Pond

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About

True stories that make math and science clear. Story Problem is for curious adults, parents helping with schoolwork, and anyone ready to understand the subjects they may have missed the first time around. No notes. No prerequisites. Just listen.

Information

  • Creator
    Behi Rabbani, MD
  • Years Active
    2026
  • Episodes
    16
  • Rating
    Clean
  • Copyright
    © 2026 Story Problem
  • Show Website
    Story Problem