Combine standard function types arithmetically to create models.
Combine two functions by addition or subtraction in context
Problem
A linear fee is \(L(t)=10t~\text{dollars}\) and an account amount is \(A(t)=100(1.05)^t~\text{dollars}\) at the same time \(t\). Build \(T(t)=L(t)+A(t)\), justify the addition using units and a shared domain, interpret \(T(t)\), and explain why the unlike terms remain separate.
Big Picture
What this problem is really about
Function outputs may be added only when they use the same input and compatible units. We’ll confirm the shared time and dollar units, substitute both rules into the total, keep the linear and exponential terms separate because their variable structures differ, and check the contextual meaning at time zero.
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