Problem

Analyze the student's statement about \(V(t)=100\cdot~0.8^{t}\). Identify the parameter error, correct the coefficient and base meanings, express the recurrence with retention and decay rates, and verify them using \(V(0)\) and \(V(1)\).

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error type = coefficient/base swap; corrected = 100 is starting value and 0.8 is retained multiplier; recurrence = V(t+1)=0.8V(t), retaining 80%/decaying 20%; checks = V(0)=100, V(1)=80

error type = percent error; corrected = 0.8 is multiplier; recurrence = multiply by 0.8; decay = 80%; checks = V(0)=100, V(1)=80

error type = no error; corrected = 0.8 is starting value; recurrence = V(t+1)=0.8V(t); checks = V(0)=100, V(1)=80

error type = coefficient/base swap; corrected = 100 is multiplier and 0.8 initial; recurrence = V(t+1)=100V(t); checks = V(0)=0.8, V(1)=80

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Analyze the student's statement about \(V(t)=100\cdot~0.8^{t}\). Identify the parameter error, correct the coefficient and base meanings, express the recurrence with retention and decay rates, and verify them using \(V(0)\) and \(V(1)\).

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