4. Meerkats are highly social small carnivores that live in southern Africa. They rely on each other to raise their young. Use the following assumptions to model the number of adult meerkats, M, in a population. You can invent parameters as necessary. - The per capita rate at which meerkats give birth to babies who survive to adulthood is a steep sigmoid function of the adult population, with higher reproductive success at higher populations. - Meerkats die of natural causes at a constant per capita rate d. - Meerkats are preyed upon by eagles and jackals. These predators have many other prey, so their population does not depend on the meerkat population. - The rate at which jackals prey on meerkats is a nonsigmoid saturating function of the meerkat population. - The rate at which eagles prey on meerkats is a sigmoid function of the meerkat population. The sigmoid is not very steep. 5. The garibaldi is a large orange fish that lives off the coast of California and Baja Califor nia. Use the assumptions below to write a differential equation for the size of an adult garibaldi population. - The number of adults joining a population is the number of eggs laid times the fraction that hatch times the fraction that survive to adulthood. - Garibaldis lay eggs at a constant per capita rate, b. - Because garibaldis sometimes eat their own eggs, the fraction of eggs that hatch is a declining sigmoid function of the adult population. - Larval garibaldis float as plankton before becoming adults and joining a population. Thus, the number of individuals joining a population is proportional to the number that hatched six years earlier, with proportionality constant r. - Adult garibaldis die at a constant per capita rate d