Problem

Analyze the student's statement about \(P(t)=300\cdot~1.06^{t}\). Identify the parameter error, correct the coefficient and base meanings, express the recurrence and percent growth, and verify them using \(P(0)\) and \(P(1)\).

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error type = additive/multiplicative confusion; corrected = 300 is initial population and 1.06 is multiplier; recurrence = P(t+1)=1.06P(t), or 6% growth/year; checks = P(0)=300, P(1)=318

error type = percent confusion; corrected = 1.06 means 106% growth/year; recurrence = multiply by 1.06; checks = P(1)=318

error type = coefficient/base swap; corrected = 300 is yearly additive increase and 1.06 initial; recurrence = add 300; checks = P(1)=301.06

error type = no error; corrected = 1.06 people/year additive rate; recurrence = P(t+1)=P(t)+1.06; checks = P(0)=300, P(1)=301.06

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Analyze the student's statement about \(P(t)=300\cdot~1.06^{t}\). Identify the parameter error, correct the coefficient and base meanings, express the recurrence and percent growth, and verify them using \(P(0)\) and \(P(1)\).

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