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

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Using Exps & Logs in Modelling
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What defines an exponential relationship?

The variable appears in the power

In the model P=Ae−ktP = Ae^{-kt}, what does PP represent?

Population

In P=Ae−ktP = Ae^{-kt}, what is the value of PP when t=0t = 0?

AA

In exponential decay P=Ae−ktP = Ae^{-kt}, what does PP approach as tt increases?

00

To linearize P=Ae−ktP = Ae^{-kt}, what should be plotted on the yy-axis?

ln⁡(P)\ln(P)

In ln⁡(P)=−kt+ln⁡(A)\ln(P) = -kt + \ln(A), what is the gradient mm?

−k-k

After taking ln of both sides of R=kTnR = kT^n, which equation results?

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

To verify R=kTnR = kT^n, what should be plotted to obtain a straight line?

ln⁡(R)\ln(R) vs ln⁡(T)\ln(T)

From Saturn's moons data, what is the gradient nn (to 3 d.p.)?

0.6970.697

What is the value of constant kk from ln⁡(k)=12.15\ln(k) = 12.15?

1.89×1051.89 \times 10^5

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