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## Homework Statement

Suppose that an amount function ## a(t) ## is differentiable and satisfies the property

## a(s + t) = a(s) + a(t) − a(0) ##

for all non-negative real numbers ## s ## and ## t ##.

(a) Using the definition of derivative as a limit of a difference quotient, show that ## a'(t) = a'(0) ##.

(b) Show that ## a(t) = 1 + it ## where ## i = a(1) − a(0) = a(1) − 1 ##.

## Homework Equations

N/A

## The Attempt at a Solution

I do not understand what part b. expects me to do. If ## a'(t) = a'(0) ##, then I can show that equivalency using the definition of ## i ##. But, does that really show that ## a(t) = 1 + it ##? Perhaps the question is poorly worded, and it should read ## a(t) ## is a possible solution? Or am I looking at this the wrong way?