Exponential Growth and Decay

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Exponential Growth and Decay. Glacier National Park, Montana Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington. Ex. Find the equation of the curve in the xy-plane that passes through the given point and whose tangent at - PowerPoint PPT Presentation

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  • Exponential Growth and DecayGreg Kelly, Hanford High School, Richland, WashingtonGlacier National Park, MontanaPhoto by Vickie Kelly, 2004

  • Ex. Find the equation of the curve in the xy-plane thatpasses through the given point and whose tangent ata given point (x, y) has the given slope

  • The number of bighorn sheep in a population increases at a rate that is proportional to the number of rabbits present (at least for awhile.)So does any population of living creatures. Other things that increase or decrease at a rate proportional to the amount present include radioactive material and money in an interest-bearing account.If the rate of change is proportional to the amount present, the change can be modeled by:

  • Rate of change is proportional to the amount present.Divide both sides by y.Integrate both sides.

  • Integrate both sides.Exponentiate both sides.When multiplying like bases, add exponents. So added exponents can be written as multiplication.

  • Exponentiate both sides.When multiplying like bases, add exponents. So added exponents can be written as multiplication.

  • Exponential Change:If the constant k is positive then the equation represents growth. If k is negative then the equation represents decay.

  • Population GrowthIn the spring, a bee population will grow according to an exponential model. Suppose that the rate of growth of the population is 30% per month.a) Write a differential equation to model the population growth of the bees.b) If the population starts in January with 20,000 bees, use your model to predict the population on June 1st.