Modelling with Exponentials & Logarithms (AQA A-Level Mathematics): Quizzes

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Exponential Growth & Decay
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Which equation represents exponential growth or decay?

y=5e2xy = 5e^{2x}

Why is y=4e−xy = 4e^{-x} an exponential decay function?

As xx increases, yy decreases

In the formula y=y0ekty = y_0 e^{kt}, what does y0y_0 represent?

Initial value at t=0t = 0

For exponential growth y=y0ekty = y_0 e^{kt}, what must be true about kk?

k>0k > 0

Which is an application of exponential growth?

Population growth

Which is an application of exponential decay?

Radioactive decay

What is the formula for doubling time in exponential growth?

ln⁡(2)k\frac{\ln(2)}{k}

What is the formula for half-life in exponential decay?

ln⁡(2)k\frac{\ln(2)}{k}

For y=2x+3y = 2^{x+3}, what happens to yy when xx increases by 1?

yy is multiplied by 2

For y=6−x+2y = 6^{-x+2}, what happens to yy when xx increases by 1?

yy is divided by 6

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