Example

Try It 10.34: Evaluating Exponential Growth

Suppose a biologist starts an experiment with an initial population of 100100 viruses (A0=100A_0 = 100) that grows continuously at a rate of 1010% per hour (r=0.10r = 0.10). To determine the number of viruses after 2424 hours (t=24t = 24), we use the exponential growth formula: A=A0ertA = A_0 e^{rt}. Substituting the given values into the equation yields A=100e0.1024A = 100 e^{0.10 \cdot 24}, which simplifies to A=100e2.4A = 100 e^{2.4}. Evaluating this expression gives an amount of approximately 1,1021{,}102. Therefore, the biologist will find 1,1021{,}102 viruses.

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Updated 2026-05-25

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