A savings model combines growth \(800(1.05)^t\) with a subtractive account-management term \(40\log(t~+~2)\). Write \(S(t)\), then state its mathematical domain and usual practical time domain.

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S(t)=800(1.05)t-40log(t+2), with domain all real t

S(t)=800(1.05)t-40log(t), with mathematical domain t>0 and practical time domain t>=0

S(t)=800(1.05)t-40log(t+2), with mathematical domain t>-2 and practical time domain t>=0

S(t)=800(1.05)t+40log(t+2), with domain t>=0

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Curriculum context

Course: Math III
Standard: F-BF.1.b
Category: Functions
Domain: Building Functions
Objective: Combine studied function types arithmetically to build models.
Problem type: Form and interpret a combined function model from two component functions