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If (D(t)=190-kt) and (D(3)-D(12)=81), what is (k)?

Answer and explanation

Correct answer: 9

Given \(D(t)=190-kt\), we have \(D(3)=190-3k\) and \(D(12)=190-12k\). Therefore, \(D(3)-D(12)=(190-3k)-(190-12k)=9k\). Since \(9k=81\), \(k=9\). Option 12 is the difference between the time values, not the value of \(k\). Exam tip: Write both function values separately before subtracting; the constant terms often cancel out.

Related tags

Linear FunctionsLinear DecayRate Of ChangeSubstitutionPolynomialsLinear Growth And DecayIntroduction To PolynomialsMathematics

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