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Understanding Exponential Growth: Impacts of Delayed Payment and Historical Outbreaks

Explore the consequences of delayed credit card bill payments and the rapid spread of historical outbreaks through exponential growth equations. Discover the significant effects of waiting to pay bills and the exponential growth patterns of epidemics like the Black Death.

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Understanding Exponential Growth: Impacts of Delayed Payment and Historical Outbreaks

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  1. University of California Berkeley

  2. Credit Card Bill: $40,000Annual Interest: 25% What happens if he waits to pay it back? How much will he owe in 10 years? In 20 years?

  3. Credit bill after 10 years: $298,023

  4. Credit bill after 20 years: $2,775,558

  5. Why did the money he owes increase so much? Put me, x, as the exponent and you have an equation that grows and grows and grows Note: x = the number of years till paid back

  6. Exponential Growth Equation Y = a(b) x Growth or Decay Factor Starting amount

  7. The Black Death: 1348 and 1350

  8. Death Rate ≈ 75,000,000

  9. The Black Death was carried by Oriental rat fleas living on the black rats

  10. Black Death: Exponential Growth

  11. Equation for the Spread of the Black Death How many people would have died in 12 months? 1,251,091

  12. Y = 1(4x) Suppose that 1 bacteria lands in your mouth and grows by a factor of 4 each hour. Write an equation that for this situation. How many bacterium will be in your mouth after 8 hours? 1,048,576

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