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If (G(t)=100-rt) and (G(2)=G(7)+35), what is (r)?

Answer and explanation

Correct answer: \(7\)

Given \(G(2)=G(7)+35\), we have \(G(2)-G(7)=35\). Substituting \(G(2)=100-2r\) and \(G(7)=100-7r\) gives \((100-2r)-(100-7r)=5r\). Thus, \(5r=35\), so \(r=7\). If \(r=5\), the difference would be only \(25\), so it is not correct. Exam tip: subtracting function values at two times cancels the constant term \(100\).

Related tags

Linear FunctionsLinear DecayRate Of ChangePolynomialsAlgebraic EquationsLinear Growth And DecayIntroduction To PolynomialsMathematics

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