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...

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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.