Exponential Growth and Decay (HSC SSCE Mathematics Advanced): Quizzes

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Exponential growth and decay
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What is the derivative of exe^x?

exe^x

For Q=ektQ = e^{kt}, what does dQdt\frac{dQ}{dt} equal?

kQkQ

Which equation represents exponential growth where rate is proportional to population PP?

dPdt=kP\frac{dP}{dt} = kP

In Q=Q0ektQ = Q_0 e^{kt}, what does Q0Q_0 represent?

Value of QQ when t=0t = 0

For exponential decay, which form is used where kk is positive?

M=M0e−ktM = M_0 e^{-kt}

What is half-life in decay problems?

Time for half the substance to remain

If population doubles in 10 years, how do you find kk from 2P0=P0e10k2P_0 = P_0 e^{10k}?

k=110log⁡e2k = \frac{1}{10}\log_e 2

Strontium-90 has half-life 28 years. After 28 years, what proportion remains?

12\frac{1}{2}

For dPdt=kP\frac{dP}{dt} = kP, what is the rate of increase when P=8000P = 8000 and k=0.22k = 0.22?

17601760 per year

To find when 10P0=P0ekt10P_0 = P_0 e^{kt}, what is tt equal to?

log⁡e10k\frac{\log_e 10}{k}

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