Exponential Growth and Decay (VCE SSCE Mathematical Methods): Quizzes

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Exponential Growth and Decay
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In the formula A=A0ektA = A_0e^{kt}, what does A0A_0 represent?

The initial quantity at time t=0t = 0

What does a positive rate constant (k>0k > 0) indicate in A=A0ektA = A_0e^{kt}?

Exponential growth

In the form A=A0btA = A_0b^t, decay occurs when bb satisfies which condition?

b<1b < 1

What is generation time (TDT_D) in bacterial growth?

Time for the population to double

Which formula models bacterial cells dividing into two every TDT_D minutes?

N=N02tTDN = N_0 2^{\frac{t}{T_D}}

In radioactive decay A=A0ektA = A_0e^{-kt}, why is there a negative sign in the exponent?

To make it a decay model (kk is positive)

What does the half-life of a radioactive substance measure?

Time for half the material to decay

A population increases at 11% per annum. What is the multiplier bb in P=P0btP = P_0b^t?

1.111.11

A population decreases at 5% per annum. What multiplier represents this change?

0.950.95

Why store exact values in calculators rather than rounded approximations?

To ensure accuracy in later calculations

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