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

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Using Exps & Logs in Modelling
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Which equation shows an exponential relationship?

y=5e7ty = 5e^{7t}

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

A constant

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

AA

To linearize P=Ae−ktP = Ae^{-kt}, what is the first step?

Take natural logarithms of both sides

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

−k-k

To linearize R=kTnR = kT^n, what should be plotted for a straight line?

ln⁡(R)\ln(R) vs ln⁡(T)\ln(T)

In the linearized form of R=kTnR = kT^n, what does the gradient represent?

nn

If Δy=2.65\Delta y = 2.65 and Δx=3.8\Delta x = 3.8, what is nn?

0.6970.697

If the y-intercept is ln⁡(k)=12.15\ln(k) = 12.15, what is kk?

e12.15e^{12.15}

What is the confirmed relationship between RR and TT for Saturn's moons?

R=1.89×105×T0.697R = 1.89 \times 10^5 \times T^{0.697}

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