Question

A bacteria culture is started with 100 bacteria. After 7 hours, the population has grown to 600 bacteria. If the population grows exponentially, Find the rate of growth in percent ______ %

Answer 1

The rate of growth is approximately 34.3%.

Step-by-step explanation:

Exponential growth is a concept often observed in bacteria. In this case, the initial population of 100 bacteria grows to 600 bacteria after 7 hours. To find the rate of growth, we can use the exponential growth formula: N = N0 * ert, where N is the final population, N0 is the initial population, e is Euler's number (approximately 2.71828), r is the rate of growth, and t is the time in hours. We can rearrange the formula to solve for the rate of growth (r): r = (ln(N) - ln(N0)) / t. Substituting the given values, r = (ln(600) - ln(100)) / 7. Using a calculator, we can find that r ≈ 0.343, or 34.3%.

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