# Calculus: Chain Rule – #26773

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?