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Growth and Decay

Explore practical applications of exponential growth and decay concepts in finance, demographics, and depreciation scenarios with detailed equations and calculations.

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Growth and Decay

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  1. Growth and Decay

  2. Exponential Growth • Initial amount increases by the same percent over a given period of time • General equation: y = C(1 + r) y = final amount C = initial amount r = rate of change(decimal) t = time

  3. In 1971, there were 294,105 females participating in high school sports. Since the, that number has increased an average of 8.5% per year. • Write an equation to represent the number of females participating in high school sports since 1971 • According to the equation, how many females participated in high school sports in the year 2001?

  4. Compound Interest • Compound interest is a special application of exponential growth • Equation: A = P(1 + ) A = amount of investment P = principal r = annual rate of interest(decimal) n = # of times interest is compounded each year t = # of years money is invested

  5. In 1626, Peter Minuit, governor of the colony of New Netherland, bought the island of Manhattan from the Native Americans for beads, cloth, and trinkets work 20 Dutch guilders ($24). If the money the Native Americans received for Manhattan had been invested at 6% per year compounded semiannually, how much money would there be in the year 2026?

  6. Exponential Decay • The original amount decreases by the same percent over a period of time. • General equation: y = C(1 - r) y = final amount C = initial amount r = rate of decay(decimal) t = time

  7. In 1950, the use of coal by residential and commercial users was 114.6 million tons. Many businesses now use cleaner sources of energy. As a result, the use of coal has decreased by 6.6% per year. • Write an equation to represent the use of coal since 1950. • Estimate the estimated amount of coal that will be used in 2015.

  8. Depreciation • A farmer buys a tractor for $50,000. If the tractor depreciates 10% per year, find the value of the tractor in 7 years.

  9. Practice Page 563 # 4 - 8

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