Find the equation of the curve for the given slope and point through which it passes. Slope given by -2y + e*; passes through (0, 8) O y = eX + 7e2x O y = ex + 7e-4x O y = eX + 7e-2x O y = e* + 7ex Solve the problem. dy/dt = ky + f(t) is a population model where y is the population at time t and f(t) is some function to describe the net effect on the population. Assume k = 0.02 and y= 10,000 when t = 0. Solve the differential equation of %3D y when f(t) = -18t. %3D y = 900t + 45,000 - 35,000e-0.02t y = 900t + 45,000 - 35,000e0.02t O y = -900t + 45,000 - 35,000e-0.02t O y = -900t - 45,000 - 35,000e0.02t Solve the problem. In a chemical reaction, the rate at which the amount of a reactant changes with time is proportional to the amount present, such that dv = -0.7y, when t is measured in hours. If dt there are 70g of reactant present when t = 0, how many grams will be left after 3 hours? Give your answer to the nearest tenth of a gram. O 0.1 g O 4.3 g O 12.9 g O 8.6 g