The per capita growth rate r (on an annual basis) of a population of grazing animals is a function of V, the amount of vegetation available. A positive value of r means that the population is growing, whereas a negative value of r means that the population is declining. For a certain species of kangaroo of Australia, the relationship is given as r = 0.5 − 2e−0.007V. Here V is the vegetation biomass, measured in pounds per acre. (a) Draw a graph of r versus V. Include vegetation biomass levels up to 1000 pounds per acre.         (b) The population size will be stable if the per capita growth is zero. At what vegetation level will the population size be stable? (Round your answer to two decimal places.)   lb/acre

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.