(See Solution) Suppose you invest in a scheme whose future value after t years is given by F=e^0.01t+0.005t^2 for each dollar invested. Answer the questions
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).
- Find \(\frac{dF}{dt}\)
- Find the percentage rate of change.
- How fast is the interest rate increasing?
- How long does it take for an initial investment of $10,000 to double? Quadruple?
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