Question: Suppose you invest in a scheme whose future value after t years is given by \(F={{e}^{0.01t+0.005{{t}^{2}}}}\) for each dollar invested. Answer the questions below, showing your work (5 points each).

(a) Find \(\frac{dF}{dt}\)

(b) Find the percentage rate of change.

(c) How fast is the interest rate increasing?

(d) How long does it take for an initial investment of $10,000 to double? Quadruple?