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- Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce at an initial rate of 3 parakeets per month. Write a differential equation for the population P assuming logistic growth, where the woodland can support at most 500 parakeets. (Do not round any coefficients.) dP/dt =Find the differential equation of the Family of lines where x-intercept is equal to y-intercept.
- A mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this mold, and 10 hours later there is 8oz. When is there 15oz of the mold?The total number of reported cases of an illness in a large city days after the start of an outbreak is modeled by the function y = F(t) that is a solution to the logistic differential equation dy/dt= (1/5600)y(1400-y). If there are 5 reported cases of the illness initially, what is the limiting value for the total number of reported cases of the illness as t increases?3. Ununoctium decays naturally at the rate proportional to the original quantity. If there are 20 grams initially, and after 10 years, 0.6% of the original amount decomposed, design an equation that will represent the amount of remaining element at any given time.
