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What is the formula for exponential growth?
If I put $1 into a savings account with 100% interest per year for 5 years, how much money will I have?
LEARNING TARGET
LEARNING TARGET
I can derive Euler's number and explain its significance in the universe.
I can derive Euler's number and explain its significance in the universe.
I DO
I DO
follow along with me here...
follow along with me here...
Imagine you have a savings account with $1 and it pays 100% interest per year. What will we have after 1 year?
Banks actually pay interest more often than that. What if it pays twice per year? Every month? Every day? Every minute? What if it happens constantly?
This is what happens when things grow or decay with respect to their size: the number of proportional growth or decay.
Where does this show up in the world?
Where does this show up in the world?
Compounding interest
Probability analysis (especially very small probabilities)
Population growth
Radioactive decay
Sinusoidal functions (sound waves, light waves, radio waves, harmonic motion like springs, AC power, pendulum clocks, ocean waves, the movement of a guitar string when you pluck it, circuits)
Temperature decrease
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WE DO
Let's try to derive e using another method:
Let's try to derive e using another method:
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YOU DO
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