Two investment options each begin with an initial principal of (C ) dollars at time…
MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
Two investment options each begin with an initial principal of C dollars at time t=0 years.
Option 1: V1(t)=Ce0.05t.
Option 2: V2(t)=Cat, where a>1 is a constant.
Answer the following questions.
(1) Describe verbally how the instantaneous growth rate of each investment depends on its current value.
(2) Given that the two investments have the same instantaneous growth rate at t=0, derive an equation relating a to the constant 0.05.
(3) Without further numerical calculation, determine which investment will eventually yield the larger value as t becomes large. Justify your conclusion using your understanding of derivatives of exponential functions.