1. Consider a population with the following characteristics; initial biomass concentration of 200 mg/L, maximum specific growth rate of 1/day, and respiration rate coefficient of 0.05/day. (a) Assume logistic growth. Determine the population's biomass (in units of mg/L) after 2, 10, 100, and 10,000 days if the carrying capacity is reported to be 5,000 mg/L. (b) Assume exponential growth. Determine the population's biomass (in units of mg/L) after 2, 10, 100, and 10,000 days. 2. A population having a biomass of x mg/L at t=0 days reaches a biomass of 139 at t = 10 days. Assuming exponential growth, calculate the value of the specific growth rate. (where x = Section number-50) 3. The rate of increase for the human population in Mexico was 1.5 percent per year. (a) How long would you expect that it would take for their population to double from its current level of 116 million people? (b) What might prevent the population from reaching this level? 4. Determine the expected population for a rural community of 1,500 people after 15 years if the community is losing population at a rate of 1%/y because of migration to urban areas. The birth rate is 20 per thousand per year and the death rate is 0.5 percent per year. 5. When food supplies have been exhausted, populations die away exponentially, which is analogous to the exponential growth model. For a decaying population of bacteria with an initial biomass of 100 mg/L and a k, = 0.4/day, calculate the time necessary to reduce the population size to 10 mg/L. 6. The 2012 Living Planet Report from the World Wildlife Fund (WWF, 2012) reported that in the year 2008, the Earth's total biocapacity was 12.0 billion global hectares, which equates to 1.80 global hectares per person. In contrast, humanity's ecological footprint was reported to be 18.2 billion global hectares, which equates to 2.74 global hectares per person. (a) Using these values, how many years would it take the Earth to fully regenerate the renewable resources that humanity consumed in 1 year (assuming no human consumption in the regeneration year)? (b) "Ecological Overshoot" is a term that describes when the global ecological footprint is larger than the Earth's biocapacity. What was the "ecological overshoot" in 2008 reported in global hectares per person?