Consider a population P = P(t) with constant relative birth and death rates and β, respectively, and a constant emigration rate m, where , β, and m are positive constants. Assume that > β. Then the rate of change of the population at time t is modeled by the differential equation dP dt = kP − m where k = − β. (a) Find the solution of this equation that satisfies the initial condition P(0) = P0. (Write an equation involving P, P0, k, m, and t.)

Martin likes to make flower bouquets that have 3 daffodils and 4 tulips per vase. a daffodil has a mass of d grams, a tulip has a mass of t grams, and the vase has a mass of u grams. the expression 5(3d + 4t + v) describes the mass of 5 bouquets. match each amount in the situation with the expression that represents it. situation expression number of bouquets mass of one bouquet mass of the tulips in one bouquet 4t mass of the daffodils in one bouquet 3d + 4t + v

An appliance store sells lamps at $95.00 for two. a department store sells similar lamps at 5 for $250.00. which store sells at a better rate

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =