Exponents & Logarithms
Where exponents and logarithms show up in real life
15 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
Exponents & LogarithmsCompound interest: money that grows on itself
Interest earns interest. Exponents explain why saving early wins.
Exponents & LogarithmsBrightness vs. distance: the inverse-square law
Move a light twice as far and it gives a quarter of the light. Photographers call that two stops.
Exponents & LogarithmsLoan payments: what a mortgage really costs
One formula sets every car, student, and home loan payment. See where the interest goes.
Ratios & ProportionsRunning pace: from your 5K to a marathon time
Pace is a ratio. Predicting a longer race takes an exponent, because you slow down.
Exponents & LogarithmsCooling coffee: when is it drinkable?
Hot things cool fast, then slower and slower. Exponential decay predicts the sip.
Exponents & LogarithmsDecibels: why two speakers aren’t twice as loud
Sound is measured on a log scale. Double the speakers: +3 dB. Double the distance: −6 dB.
Exponents & LogarithmsCredit card payoff: how many months until it’s gone?
A logarithm answers “how long?” See why minimum payments take forever.
Exponents & LogarithmsThe rocket equation: why rockets are almost all fuel
Speed grows with the logarithm of the fuel. Double the tank and you get far less than double the speed.
Exponents & LogarithmsOrbits: how fast to go around and never come down
An orbit is falling and missing the ground. Square roots and a 3/2 power set the speed and the period.
Exponents & LogarithmsE6B density altitude, exact: standard atmosphere and humidity
The full standard-atmosphere formula, plus the dew point. Humid air is lighter, so it flies higher.
Exponents & LogarithmsE6B true airspeed: why you’re faster than the dial says
The airspeed indicator feels air pressure, not speed. Thin air at altitude makes true airspeed higher.
Differential Equations & TransformsWhen will my coffee wear off?
Each cup rises, then fades by half every few hours. Cups stack, and the Laplace transform says why they simply add.
Exponents & LogarithmsRapid cooling: 135 °F to 70 °F in two hours
Cooling slows as food nears the fridge temperature. A logarithm says how long it takes, and why shallow pans win.
PolynomialsIs this investment worth it? The rate of return is a polynomial’s root
Money today and money later add up to a polynomial. The rate that makes it zero is the investment’s internal rate of return.
Exponents & LogarithmsThe Bartz equation: how regenerative cooling keeps a rocket throat from melting
Heating grows with chamber pressure to the 0.8 power and peaks at the throat. The fuel flows through the wall to carry it away.