Example

Example: Evaluating Continuous Exponential Growth of a Bacteria Population

Suppose a researcher starts an experiment with an initial population of 50 bacteria (A0=50A_0 = 50) that grows continuously at a rate of 15% per hour (r=0.15r = 0.15). To determine the number of bacteria after 8 hours (t=8t = 8), we use the exponential growth formula: A=A0ertA = A_0 e^{rt}. Substituting the given values into the equation yields A=50e0.158A = 50 e^{0.15 \cdot 8}, which simplifies to A=50e1.2A = 50 e^{1.2}. Evaluating this expression gives an amount of approximately 166. Therefore, the researcher will find approximately 166 bacteria.

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Updated 2026-06-18

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