Calc06_4 - Glacier National Park Montana Photo by Vickie Kelly 2004 6.4 Exponential Growth and Decay Greg Kelly Hanford High School Richland Washington

Calc06_4 - Glacier National Park Montana Photo by Vickie...

This preview shows page 1 - 6 out of 12 pages.

6.4 Exponential Growth and Decay Greg Kelly, Hanford High School, Richland, Washington Glacier National Park, Montana Photo by Vickie Kelly, 2004
The number of bighorn sheep in a population increases at a rate that is proportional to the number of sheep 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: dy ky dt =
dy ky dt = 1 dy k dt y = 1 dy k dt y = ln y kt C = + Rate of change is proportional to the amount present. Divide both sides by y . Integrate both sides.
1 dy k dt y = ln y kt C = + Integrate both sides. Exponentiate both sides. When multiplying like bases, add exponents. So added exponents can be written as multiplication. ln y kt C e e + = C kt y e e =
ln y kt C e e + = C kt y e e = Exponentiate both sides.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture