Your company has developed a new product, and your marketing department has predicted how it will sell. Let y(t) be the (monthly) sales of the product after t months. (a) Write a differential equation that says that the rate of growth of the sales will be eight times the onehalf power of the sales. I y: (b) Write an initial condition that says that at time t = 0 sales were $10,000. Y(0) = (c) Solve this differential equation and initial value. y: (d) Use your solution to predict the sales (in dollars) at time t = 12 months. (Round your answer to the nearest whole number.) $