Using Exps & Logs in Modelling (AQA A-Level Mathematics): Flashcards

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Using Exps & Logs in Modelling
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Define exponential relationship

A relationship where the variable appears in the exponent/power

In P=AektP = Ae^{-kt}, value of PP when t=0t = 0

P=AP = A

Type of curve for P=AektP = Ae^{-kt}

Exponential decay

P=AektP = Ae^{-kt} approaches what as tt increases?

00

Rearranged form of P=AektP = Ae^{-kt} using ln

ln(P)=kt+ln(A)\ln(P) = -kt + \ln(A)

In ln(P)=kt+ln(A)\ln(P) = -kt + \ln(A), gradient mm equals?

m=km = -k

ln form of R=kTnR = kT^n

ln(R)=ln(k)+nln(T)\ln(R) = \ln(k) + n\ln(T)

In ln(R)=ln(k)+nln(T)\ln(R) = \ln(k) + n\ln(T), gradient equals?

nn

In Saturn moons example, calculated value of nn

0.6970.697

In Saturn moons example, calculated value of kk

1.89×1051.89 \times 10^5

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