y is related to x through the differential equation: dy dx = ax + bx² + dx³ and y = c when x = 0 where a = -1.1, b = 0.3, d = 2.2 and c = 2.2 Find y to one decimal place when x = 3

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.

Morphine is administreted to a patient intravenously at a rate of 2.5 mg per hour. About 34,7% of the morphine is metabolized and leaves the body each hour. Write a differential equation for the amount of morphine, M, in milligrams, in the body as a function of time, t, in hours.

The concentration of a medication M in mg/L present in the bloodstream decreases over time such that the concentration of medication is proportional to the amount of medication t hours after the first dose. The concentration of medication 30 minutes after the first dose is 80 mg/L and was decreasing at a rate of 150 mg/L per hour. Which differential equation represents this relationship? dM =-1.875M dt dM =-1.25M dt dM = -0.66M dt dM = -0.063M dt