Exponential Growth & Decay (Edexcel A-Level Mathematics): Quizzes

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Exponential Growth & Decay
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What feature indicates that a quantity grows or decays exponentially?

Variable in the index power

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

Initial value at t=0t = 0

For exponential growth using y=y0ekty = y_0 e^{kt}, what condition must kk satisfy?

k>0k > 0

How does the rate of change behave during exponential growth?

Increases as the quantity grows

What is the general formula for exponential decay?

y=y0e−kty = y_0 e^{-kt}

Which processes commonly exhibit exponential decay?

Radioactive decay & depreciation

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

To solve 3=50e−0.2t3 = 50e^{-0.2t} for tt, what operation is used after rearranging?

Take natural logarithm

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